Identifying Stationary Points (Critical Points) for a Function

Key Questions

• How do you find the stationary points of a curve?

  A stationary (critical) point #x=c# of a curve #y=f(x)# is a point in the domain of #f# such that either #f'(c)=0# or #f'(c)# is undefined. So, find f'(x) and look for the x-values that make #f'# zero or undefined while #f# is still defined there.

  Wataru · · Aug 26 2014
• What is a stationary point, or critical point, of a function?

  Definition
  A number #c# in the domain of #f# is called a critical number if #f'(c)=0# or #f'(c)# is undefined.

  I hope that this was helpful.

  Wataru · 1 · Oct 16 2014

• How do you find the stationary points of a curve?
• How do you find the stationary points of a function?
• How many stationary points can a cubic function have?
• How do you find the stationary points of the function #y=x^2+6x+1#?
• How do you find the stationary points of the function #y=cos(x)#?
• How do I find all the critical points of #f(x)=(x-1)^2#?
• Let #h(x) = e^(-x) + kx#, where #k# is any constant. For what value(s) of #k# does #h# have critical points?
• How do you find the critical points for #f(x)=8x^3+2x^2-5x+3#?
• How do you find values of k for which there are no critical points if #h(x)=e^(-x)+kx# where k is any constant?
• How do you determine critical points for any polynomial?
• How do you find all critical points (if any) if #k(t)=1/sqrt(t^2 +1)#?
• What do critical points tell you?
• How do you find critical points on a graph?
• How do you find the critical points of #f(x)=sinx+cosx#?
• How do you find the critical points of a multivariable function?
• How do you find the critical point(s) of #f(x,y) = (x-y)^2#?
• What are the critical points of #(x^2/(x^2-1))#?
• How do you find the critical point and determine whether it is a local maximum, local minimum, or neither for #f(x, y) = x^2 + 4x + y^2#?
• How do you find the critical points for #y = x^(2/3)(x^2-16) #?
• How do you find critical points for #G(x)= ^3sqrt(x²-x)#?
• What are the critical points for #f(x)=x^(2/5)(x-10)#?
• How do you find the critical points for #f(x)= x^2 + 4x - 12#?
• How do you find and classify the critical points of this differential equation #dx/dt = 2x + 4y + 4#?
• How do you find all the critical points of the function #f(x) = x^3 − 12x + 7#?
• How do you find the critical points of the function #f(x) = x / (x^2 + 4)#?
• How do you find the critical points and the open intervals where the function is increasing and decreasing for #y = xe^(x(2 - 3x))#?
• How do you find the critical points for #y=x+2x^-1#?
• How do you find the critical points of #f(x) = x - 3ln(x)#?
• What are the critical points of #f(x)= -x^2 + 3x# on the interval [0,3]?
• How do you determine whether the given critical point x=-2.5 is the location of a maximum, a minimum, or a point of inflection for #y= 2x^2 + 10x - 7#?
• How do you identify a critical point of #y = e^(x+2) – e^(2x)# and determine whether it is a local maximum or a local minimum?
• How do you locate the critical point, and determine the maxima and minima of #y=x^3-6x^2+9x-8#?
• How do you find the critical points for #x^2-5x+4# and state whether it is stable or unstable?
• How do you find the critical points for #f(x) = 2x^(2/3) - 5x^(4/3)#?
• How do you find the intervals in which #f (x) = log_7(1+x^2)# is increasing or decreasing?
• How do you find the critical points for #y = x^2(2^x)#?
• How do you use the first derivative test to determine whether the critical point is a local maximum, local minimum, or neither for #y=x^4 - 8x^2#?
• How do you find the critical points of #y=x-2sinx# on the interval #[0, pi/2]#?
• How do you find critical points for function of two variables #f(x,y)=8x^3+144xy+8y^3#?
• What are the critical points for #f(x) = xsqrt(16 - x^2)#?
• What is the difference between a critical point and a stationary point?
• How do you find on what time interval is the concentration of the drug increasing if suppose a certain drug is administered to a patient, with the percent of concentration in the bloodstream t hr later given by #K(t)= 8t / (t^2 + 1)#?
• How do you find the critical numbers of #f(x) = x^4(x-1)^3#?
• Let #f(x,y)=8x^3+y^3-6x-12y+4#, how do you determine all critical points?
• How do you use the first derivative test to determine the intervals on which #f(x)=x^4+3x^3+3x^2+1# is increasing or decreasing and whether each critical point is a local maximum, minimum or neither?
• What are the critical numbers for #f(x)= x/(x+1)#?
• What are the critical points for #f(x) = (x^2-10x)^4#?
• How do you find the critical points for the inequality #(2x+1)/(x-9)>=0#?
• How many critical points does the function #f(x) = (x+2)^5 (x^2-1)^4# have?
• If #f(x)=sinx-cosx#, what are the critical points on the interval (0,pi)?
• How do I find the critical points for the function #f(x)=7x^4-6x^2+1#?
• How do you find critical points for #f(x,y)= 2y^3+3x^3-6xy#?
• How do you find the critical points #f(x)= 2x^3 + 3x^2 - 36x + 5#?
• How do you find critical point for this equation #f(x,y)=6x^7+7y^2+8xy+9#?
• How do you find the critical points for #y = -0.1x^2 − 0.5x + 15#?
• How do you find the critical points of: #f(x)=(x)(e^(-x^2))#?
• How to find the critical points of a function #f(x,y)=xy^2-3x^2-y^2+2x+2#?
• How do you find the critical points of the function #f(x,y)=x^2+y^2+(x^2)(y)+4#?
• How do you find the critical points(using partial derivative) for #f( x , y )=x^3 + y^2 - 6x^2 + y -1#?
• How to find critical points and the using the first derivative test for #f(x) = 3x^4 - 4x^3 + 6#?
• How do you find the critical points of #h(x)=(x+1)/x#?
• How do you find the critical points for #y = 2x^3 + 3x^2 - 12x + 4#?
• How do you find the critical points if #f'(x)=2-x/(x+2)^3#?
• How do you find the critical points #f(x)= x^3 + 35x^2 - 125x - 9375#?
• How do you find the critical points for #f(x)= x^(4/3) + 4x^(1/3)+ 4x^(-2/3)#?
• How do you find critical points for the equation #(7/10)cos(x/10)#?
• How do you find the critical points of f when #f(x)= x^4/(5(x-5)^2)#?
• How do you find critical points of multivariable function #f(x,y) =x^3 + xy - y^3#?
• How do you find the critical points for #f'(x)=11+30x+18x^2+2x^3#?
• How do you find critical points for #f(x) = x^4 - 8x^3 - 16x +5#?
• How do you find the Critical Points for #x^3 + 3x^2-24x#?
• How would you find the critical points of #(x^2+1)/(x^2-4)#?
• How do you find the critical points for #y = x*sqrt(8-x^2)#?
• How do you find critical points of a logarithmic function #y = e^x - 2e^(-x) - 3x#?
• How do you find the critical points for #y = x/(x-1)^2#?
• How do you find the critical values for #f(x)=x^(2/3)+x^(-1/3)#?
• What are the critical points of #h(x)=lnsqrt(3x-2(x^2))#?
• What are the critical points of #s(t)=(e^t-2)^4/(e^t+7)^5#?
• What are the critical points of #s(t)=(e^t-2)^4(e^t+7)^5#?
• What are the critical points of #g(x)=(x+2)/(7-4x)#?
• What are the critical points of #g(x)=x/3 + x^-2/3#?
• What are the critical points of #g(x)=x^(2/5)(x-10)#?
• What are the critical points of #g(x)=e^(x^2)(x-10)#?
• What are the critical points of #f(t) = tsqrt(2-t)#?
• What are the critical points of #f(t) = e^tsqrt(2-t+t^2)#?
• What are the critical points of #f (x) = e^x + e^-(6x)#?
• What are the critical points of #f (x) = e^x + ln(6x^2+x)#?
• What are the critical points of #f (x) = log_7(1+x^2)#?
• What are the critical points of #f(x,y) = x^3 + y^3 - xy#?
• What are the critical points of #f(x,y) = e^(x^3) + y^3 - e^(xy)#?
• What are the critical points of #f(x)=x^(2/3) *e^ (x^2-4)#?
• What are the critical points of #f(x) = 6x^(2/3) + x^(5/3)#?
• What are the critical points of #f(x) = sqrt((x^2 - 4x +5))#?
• What are the critical points of #f(x) = e^x(3x^2 - 2x +5)#?
• What are the critical points of #f(x) = 3x-arcsin(x)#?
• What are the critical points of #f(x) = x^2 + 2/x#?
• What are the critical points of #f(x) = x^2e^x + 2/x^2#?
• What are the critical points of #f(x,y) =x^3 + xy - y^3#?
• What are the critical points of # f(x) = x^(1/3)*(x+8)#?
• What are the critical points of # f(x) = e^(x^(1/3))*sqrt(x+8)#?
• What are the critical points of # f(x) = e^xlnx^2#?
• What are the critical points of # f(x) = x*sqrt(8-x^2) #?
• What are the critical points of # f(x) = (x - 3sinx)^4 -xcosx#?
• How can you identify critical points by looking at a graph?
• What are critical points?
• What are the critical points of # f(x,y)=sin(x)cos(y) +e^xtan(y)#?
• What are the critical points of # f(x)=4x^3+8x^2+6x-2#?
• What are the critical points of # f(x)=3x^4+6x^3#?
• What are the critical points of # f(x)=x^(2/3)x^2 - 16#?
• What are the critical points of # f(x,y) = 1 + x^2 - cos(3y)#?
• What are the critical points of # f(x,y)=x^3 y + 4x^2 − 8y#?
• What are the critical points of #f(x)=7x^4-6x^2+1 #?
• What are the critical points of #f(x) = x / (x^2 + 4)#?
• What are the critical points of #f(x) = 2x^3-3x^2-12x#?
• What are the critical points of #f(x) = -3x^4 + 12x^3 + 6#?
• What are the critical points of #f(x) = -(2x - 2.7)/ (2 x -7.29 )^2#?
• What are the critical points of #f(x) = x(x + 1)^3#?
• What are the critical points of #f(x) = x^3 − 12x + 7#?
• What are the critical points of #f(x,y)=x^2+y^2-4x-6y+5 #?
• What is the derivative of a function equal to at a critical point?
• How do you find the critical points for #abs(x^2 -1)#?
• How do you find the critical points for #f(x)= (2x^2+5x+5)/(x+1)#?
• How do you find the critical points for #f(x)=(x^2)(x-2)^(1/3)#?
• How do you find the critical points for # f(x) = x^4 + 2x^3#?
• How do you find the critical points for # f(x)=3cos2(x-pi/4)+1#?
• How do you find the critical points for # f(x)=x^3-6x^2+12x-6#?
• How do you find the critical points for #F(x) =xe^-x#?
• How do you find the critical points for #f(x)=3e^(-2x(^2))#?
• How do you find the critical points for # y = x^3 + 12x^2 + 6x + 8 #?
• How do you find the critical points for #x^4(lnx) #?
• How do you find the critical points for #f(x)= 6x^(2/3) + x^(5/3)#?
• How do you find the critical points for #y= 2x^2 + 10x - 7#?
• How do you find the critical points for #f(x,y)=xy(1-8x-7y)#?
• What are the critical values, if any, of #f(x) = x^(2/3)+x^(-1/3) #?
• What are the critical values, if any, of #f(x) = x^3 + x^2 - x #?
• What are the critical values, if any, of #f(x) = -3x^2+x-1#?
• What are the critical values, if any, of #f(x)= x/(x+1)#?
• What are the critical values, if any, of #f(x)=xe^(-3x)#?
• What are the critical values, if any, of #f(x)=x+e^(-3^x)#?
• What are the critical values, if any, of #f(x)= x^3 + 20/x^2 + 100/ x^3 + 9x^2 + 15/x - 25 #?
• What are the critical values, if any, of #f(x)= abs(3x-4) #?
• What are the critical values, if any, of #f(x)= x^6ln(x) #?
• What are the critical values, if any, of #f(x)= x/(x^2 + 25)#?
• What are the critical values, if any, of #f(x)= x^3/sqrt(x + 25)#?
• What are the critical values, if any, of #f(x)= (2-x)/(x+2)^3#?
• What are the critical values, if any, of #f(x)= 5x^2 +4x#?
• What are the critical values, if any, of #f(x)= 3x^3+7x^2-8x#?
• What are the critical values, if any, of #f(x)= (x^2+6x-7)^2#?
• What are the critical values, if any, of #f(x)= x^(3/4) - 2x^(1/4)#?
• What are the critical values, if any, of #f(x)= -2 x^3 + 27 x^2 - 48 x + 7#?
• What are the critical values, if any, of #f(x)= 5x + 6x ln x^2#?
• What are the critical values, if any, of #f(x)= x^2*(1 + 3 ln x)#?
• What are the critical values, if any, of #f(x)= (x+1) /(x^2 + x + 1)#?
• What are the critical values, if any, of #f(x)= (x+1)^2 /(-x^2 - x)#?
• What are the critical values, if any, of #f(x)=(x^2-3) / (x+3)#?
• What are the critical values, if any, of #f(x)=2secx + tan x in[-pi,pi]#?
• What are the critical values, if any, of #f(x)=(x-5)/(x^2+8)#?
• What are the critical values, if any, of #f(x)=(x^2-5x)/(x^2-2)#?
• What are the critical values, if any, of #f(x)=(4x)/(x^2 -1)#?
• What are the critical values, if any, of #f(x)=(3x^2+2x+5)/(4x^2+2x+1)#?
• What are the critical values, if any, of #f(x)=x^(4/5) (x − 3)^2#?
• What are the critical values, if any, of #f(x) = f(x) = x^{2}e^{15 x}#?
• What are the critical values, if any, of #f(x) = (x - 1) / (x + 3) -sqrt(x^2-3)#?
• What are the critical values, if any, of #f(x) = xe^(2x)#?
• What are the critical values, if any, of #f(x) = e^(2x) - 2xe^(2x)#?
• What are the critical values, if any, of # f(x)= |x^3 - 3 x^2 + 2| #?
• What are the critical values, if any, of # f(x)= sin|x|#?
• What are the critical values, if any, of # f(x)= x cos x −3 sin x +2x in [0,2pi]#?
• What are the critical values, if any, of # f(x)= cotx-sinx+tanx in [0,2pi]#?
• What are the critical values, if any, of # f(x)= sin^2x +cos^2x in [0,oo]#?
• What are the critical values, if any, of # f(x)= x^2sinx +sinxcos^2x in [0,pi]#?
• What are the critical values, if any, of # f(x)= 4 x ^ (5/4 ) - 8 x ^ (1/4)#?
• What are the critical values, if any, of # f(x)= (x-2)/(x^2-4)+2x#?
• What are the critical values, if any, of # f(x)=x^3 + 6x^2 − 135x#?
• What are the critical values, if any, of # f(x)=x^3 + 6x^2 − 15x#?
• What are the critical values, if any, of # f(x)=cscxtanx-sqrt(xcosx) in [0,2pi]#?
• What are the critical values, if any, of # f(x)=4x^3-12x#?
• What are the critical points, if any, of #f(x,y) = 5x^2 + 4xy + 3y^2 - 52x - 56y + 13#?
• What are the critical points, if any, of #f(x,y) = 2x^3 - 6x^2 + y^3 + 3y^2 - 48x - 45y#?
• What are the critical numbers of #f(x) = x^2*(1 + 3 ln x)#?
• What are the critical numbers of #f(x) = 1-x/(3-x^2)#?
• What are the critical points of #f(x) =(x^2-4x+5)/(x-3)#?
• What are the critical points of #f(x) =(x^2-2x)/(x-1)^2#?
• What are the critical points of #f(x) =ln(xe^x)#?
• What are the critical points of #f(x) =x^2ln(x/e^x)#?
• What are the critical points of #f(x) =e^x-(xlnx)/(x-2)^2#?
• What are the critical points of #f(x) =e^x-x^2e^(x^2)#?
• What are the critical points of #f(x) =2e^(3x)-3xe^(2x)#?
• What are the critical points of #f(x) =xsqrt(e^x-3x)#?
• What are the critical points of #f(x) = 1/sqrt(x+x^2-3)#?
• What are the critical points of #f(x) = x/(e^(sqrtx)#?
• What are the critical points of #f(x) = sqrt(e^(sqrtx)-x^2)#?
• What are the critical points of #f(x) = sqrt(e^(sqrtx)-sqrtx)#?
• What are the critical points of #f(x) = sqrt(sqrt(x)e^(sqrtx)-sqrtx)-sqrtx#?
• What are the critical points of #f(x) =e^(e^x)#?
• What are the critical points of #f(x) =x^(e^x)#?
• What are the critical points of #f(x) =x^(x^2)#?
• What are the critical points of #f(x) =1/(xe^x)-e^(2x)/x#?
• What are the critical values of #f(x)=4x^2+2x+1#?
• What are the critical values of #f(x)=3x^2+2x+5#?
• What are the critical values of #f(x)=(3-x)^2-x#?
• What are the critical values of #f(x)=x/sqrt(x^2+2)-(x-1)^2#?
• What are the critical values of #f(x)=1/sqrt(x^2+4)-ln(x^2+4)#?
• What are the critical values of #f(x)=x-xsqrt(e^x#?
• What are the critical values of #f(x)=xe^(2x+5)-x^3e^(-x^2-x)#?
• What are the critical values of #f(x)=x/e^(x+x^2)-x^2#?
• What are the critical values of #f(x)=(x-lnx)/e^(x+ln(x^2))-x#?
• How do you find the critical numbers of #x^4-2x^3-3x^2-5#?
• How do you find the critical numbers of # y= x^2*(1 + 3 ln x)#?
• How do you find the critical numbers of #1/(t^2+3)#?
• How do you find the critical numbers of # f(t)=t(4-t)^(1/2)#?
• How do you find the critical numbers of #f(x)=(x^2+6x-7)^2#?
• How do you find the critical numbers of #f(x)=x^2-6x#?
• How do you find the critical numbers of #9x^3 - 25x^2#?
• How do you find the critical numbers of #f(x)= 2x^3 + 3x^2-12x#?
• How do you find the critical numbers of #y= 2x-tanx#?
• How do you find the critical numbers of #f(x)=|x+3|-1#?
• How do you find the critical numbers of #f(x)=sinxcosx#?
• How do you find the critical numbers of #y = (x^2-4)/(x^2-2x)#?
• How do you find the critical numbers of #y = abs(x^2 -1)#?
• How do you find the critical numbers of #f(x)=x^(2/3)+x^(-1/3)#?
• How do you find the critical numbers of #f(x) = x + 2sinx#?
• How do you find the critical numbers of #y = sin^2 x#?
• How do you find the critical numbers of #y = cos x - sin x#?
• How do you find the critical numbers of #f(x) = (4 x - 6)e^{-6 x} #?
• How do you find the critical numbers of # f(x)=x^(1/5)-x^(-4/5)#?
• How do you find the critical numbers of #f(x)=(x^2)(e^(11x))#?
• How do you find the critical numbers of #f(x)=ln(x^4+27)#?
• How do you find the absolute maximum and absolute minimum values of f on the given interval #f(x) = ln(x^2 + 3x + 9)# and [-2, 2]?
• How do you find the absolute maximum and absolute minimum values of f on the given interval #f(x) = x^5 - x^3 - 1# and [-1, 1]?
• How do you find the intervals of concavity and increasing or decreasing for #f(x)=x^(5)ln(x)#?
• Question #c7a86
• How do you find the equation for a curve between two points?
• How do you find the equation for a curve between two points?
• How do you use the first derivative to determine where the function #f(x)= 3 x^4 + 96 x# is increasing or decreasing?
• What is the first derivative, and the integral of x!?
• How do you use the first derivative test to find the local max and local min values of #f(x)= -x^3 + 12x#?
• What is the first derivative and second derivative of #x^4 - 1#?
• How do you find the critical numbers for #f(x)= x^(-8) ln x# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x) = (x - 1 )/( x + 3)# to determine the maximum and minimum?
• How do you find the critical numbers for #(2-x)/(x+2)^3# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x)=x^2-6x# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x) = |x + 3| - 1# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x) = x^(1/3)*(x+3)^(2/3)# to determine the maximum and minimum?
• How do you find the critical numbers for #h(x) = sin^2 x + cos x# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x) = 3x^4 + 4x^3 - 12x^2 + 5# to determine the maximum and minimum?
• How do you find the critical numbers for #root3((x^2-x))# to determine the maximum and minimum?
• How do you find the critical numbers for #g(t)=abs(3t-4)# to determine the maximum and minimum?
• How do you find the critical numbers for #cos (x/(x^2+1))# to determine the maximum and minimum?
• How do you find the critical numbers for #x^4-2x^3-3x^2-5# to determine the maximum and minimum?
• How do you find the critical numbers for #9x^3 - 25x^2# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x) = x + 2sinx# to determine the maximum and minimum?
• How do you find the critical numbers for #y = x * sqrt( 9 - x^2)# to determine the maximum and minimum?
• How do you find the critical numbers for #y = (x^2-4)/(x^2-2x)# to determine the maximum and minimum?
• How do you find the critical numbers for #y = e^(3x^4-8x^3-18x^2 )# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x)= x^3 + x^2 + x# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x) = x^(-2)ln(x)# to determine the maximum and minimum?
• How do you find the critical numbers for # f(x) = x^(1/3) (x+4)# to determine the maximum and minimum?
• How do you find the critical numbers for #y = x/(x^2 + 25)# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x) = x-2ln(x)# to determine the maximum and minimum?
• How do you find the critical numbers for #g(t) = t sqrt(4-t) # to determine the maximum and minimum?
• How do you find the critical numbers for #h(p) = (p - 2)/(p^2 + 3)# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x)= x sqrt (2x+1)# to determine the maximum and minimum?
• How do you find the critical numbers for #h(t) = (t^(3/4)) − (9*t^(1/4))# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x)= x^2 - 4# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x)= (x+3) / x^2# to determine the maximum and minimum?
• How do you find the critical numbers for #f(x)= (x-1) e^x# to determine the maximum and minimum?
• Question #5a24c
• What is it equal to?
• How do you find the critical numbers of #1/(t^2+3)#?
• How do you find the critical numbers of #e^(-x^2)#?
• How do you find the critical numbers of #y=cos x + sin 2x#?
• How do you find the critical numbers of #g(θ) = 4 θ - tan(θ)#?
• How do you find the maximum value of #f(x) = -3x^2 +30x -50#?
• How do you find the maximum value of #y=x^2+2x+3#?
• How do you find the maximum value of # y = -x^2 + 8x - 4#?
• How do you find the maximum value of # Y= -2(x+5)²-8#?
• How do you find the maximum value of #f(x) = sinx ( 1+ cosx) #?
• How do you find the maximum value of #f(x) = sinx+cosx#?
• How do you find the maximum value of #y = -2x^2 + 36x - 177#?
• How do you find the maximum value of #3x^2-x^3#?
• How do you find the maximum value of #f(x)=2sin(x)+cos(x)#?
• How do you find the maximum value of #y = −2x^2 − 3x + 2#?
• How do you find the maximum value of #f(x)=20e^(-2x)*sin(3x) #?
• How do you find the maximum value of #-3(sqrt(x-9) + 12)#?
• How do you find the maximum or minimum value of #y=2x^2 +32x - 4#?
• Does the function #f(x) = x^2 - 2x + 2# have a maximum or minimum value?
• How do you find the maximum value of the function #f(x,y,z)= x+2y-3z# subject to the constraint #z=4x^2+y^2#?
• What is the maximum value of #f(x)=-3(x+3)^2+8#?
• What is the maximum value of #y=-3sinx+2#?
• What is the maximum value of #5sin(t) + 12cos(t)#?
• What is the maximum value of # f(x)= 3x^2 - x^3#?
• Does the function #f(x)=-8x +x^2# have a maximum or minimum?
• Does the function #f(x)=x^2 + 2x +15# have a maximum or minimum?
• What is the maximum value that the graph of #z=10-12w-2w^2#?
• What is the maximum value that the graph of #f(x)=4x^2-24x+1#?
• What is the maximum value that the graph of #f(x)= -x^2+8x+7#?
• What is the maximum value that the graph of #y= x^2 -4x#?
• What is the maximum value that the graph of #y= -x^2 +5x -1#?
• What is the maximum value that the graph of #sin^4x+cos^4x#?
• What is the maximum value that the graph of #y=-x^2+6x-8#?
• What is the maximum value that the graph of #-3x^2 - 12x + 15#?
• Given #p_1=(1,1), p_2=(6,3), p_3=(4,5)# and the straight #y = 1.5-(x-4)# what is the point #p=(x,y) # pertaining to the straight, minimizing #norm(p_1-p) + norm(p_2-p)+norm(p_3-p)#?
• What interval is #F(x) = (x^2)/(x^2+3)# increasing, decreasing?
• The derivative of a function f is given by f'(x)= (x-3)e^x for x>0 and f(x)=7? a.) The function has a critical point at x=3. At this point, does f have a relative minimum or neither?
• How do you find the critical points for #xe^x#?
• How do you find the critical points for #f(x) = x^3 - 15x^2 + 4# and the local max and min?
• How do you find the critical points for # x+2x^-1# and the local max and min?
• How do you find the critical points for #f(x)= -(sinx)/ (2+cosx) # and the local max and min?
• How do you find the critical points for #f(x)= (sinx) / (cosx-2)# and the local max and min?
• How do you find the critical points for #f(x)=3sin^2 x# and the local max and min?
• How do you find the critical points for #f(x) = x - 3ln(x)# and the local max and min?
• How do you find the critical points for #f(x, y) = x^2 + 4x + y^2# and the local max and min?
• How do you find the critical points for #xlnx# and the local max and min?
• How do you find the critical points for #f(x)=x^(8)# and the local max and min?
• How do you find the critical points for #f(x)=sinx cosx # and the local max and min in #0 ≤ x < 2pi?
• How do you find the critical points for #f(x) = (x^2-10x)^4# and the local max and min?
• How do you find the critical points for #f(x) = 2x^(2/3) - 5x^(4/3)# and the local max and min?
• How do you find the critical points for #-2/9x^3 -2/3x^2+16/3x+160/9# and the local max and min?
• How do you find the intervals of increasing/decreasing of #F(x)= (x^2-1)^3#?
• How do you find the critical points of #f'(x)=15-5x#?
• How do you find the critical points of #h'(x)=x^2+8x-9#?
• How do you find the critical points of #g'(x)=3x^2-6x^2#?
• How do you find the critical points of #d'(x)=x^2+2x-4#?
• How do you find the critical points of #k'(x)=x^3-3x^2-18x+40#?
• How do you find the critical points of #b'(x)=x^3+3x^2-4x-12#?
• Question #9cb16
• Question #efd90
• How do you find all local maximum and minimum points given #y=x^2-x#?
• How do you find all local maximum and minimum points given #y=x^3-9x^2+24x#?
• How do you find all local maximum and minimum points given #y=x^4-2x^2+3#?
• How do you find all local maximum and minimum points given #y=3x^4-4x^3#?
• How do you find all local maximum and minimum points given #y=(x^2-1)/x#?
• How do you find all local maximum and minimum points given #y=x^2-98x+4#?
• Does #f(x)=2x^2-8x+5# have a maximum or a minimum? If so, what is it?
• How do you find all critical numbers of the function #f(x)=x^(4/5)(x-4)^2#?
• How do you find all critical numbers for the function #f(x)= (x + 2)^3*(x -1)^4#?
• How do you find the critical points of #f(x)=(x-10)^2(x+5)#?
• Analyse the function #f(x) = (1+x)^(2/3)*(3-x)^(1/3)# for extreme values, zeros and points of discontinuity, if any?
• Question #5d180
• Question #87d49
• Question #826c5
• Question #c6955
• When using the first derivative test to find the critical points of a function, do you always have to include #x=0?#
• Question #e73e6
• Question #12f8c
• A parabola has a critical point at #(25, -14)#. It also has a tangent with equation #y=-18x+20 #. What is the equation of the parabola?
• Identify the Critical Points for the function? : # f(x,y) = 3xy-x^3-3y^2 #
• The curve of #y=f(x)# where #f(x) = x^2 + ax + b # has a minimum at #(3,9)#. Find #a# and #b#?