Identifying Turning Points (Local Extrema) for a Function

Key Questions

• How do you find the extreme values of the function and where they occur?

  Answer:

  See below.

  Explanation:

  To find extreme values of a function `f`, set `f'(x)=0` and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins.

  For example. consider `f(x)=x^2-6x+5`. To find the minimum value of `f` (we know it's minimum because the parabola opens upward), we set `f'(x)=2x-6=0` Solving, we get `x=3` is the location of the minimum. To find the y-coordinate, we find `f(3)=-4`. Therefore, the extreme minimum of `f` occurs at the point `(3,-4)`.

  Teddy · 1 · Jul 5 2018
• How many turning points can a cubic function have?

  Any polynomial of degree `n` can have a minimum of zero turning points and a maximum of `n-1`. However, this depends on the kind of turning point.

  Sometimes, "turning point" is defined as "local maximum or minimum only". In this case:

  • Polynomials of odd degree have an even number of turning points, with a minimum of 0 and a maximum of `n-1`.
  • Polynomials of even degree have an odd number of turning points, with a minimum of 1 and a maximum of `n-1`.

  However, sometimes "turning point" can have its definition expanded to include "stationary points of inflexion". For an example of a stationary point of inflexion, look at the graph of `y = x^3` - you'll note that at `x = 0` the graph changes from convex to concave, and the derivative at `x = 0` is also 0.

  If we go by the second definition, we need to change our rules slightly and say that:

  • Polynomials of degree 1 have no turning points.
  • Polynomials of odd degree (except for `n = 1`) have a minimum of 1 turning point and a maximum of `n-1`.
  • Polynomials of even degree have a minimum of 1 turning point and a maximum of `n-1`.

  So, in part, it depends on the definition of "turning point", but in general most people will go by the first definition.

  CJ · 8 · Sep 6 2014
• What is special about a turning point?

  For a differentiable function `f(x)`, at its turning points, `f'` becomes zero, and `f'` changes its sign before and after the turning points.

  ---

  I hope that this was helpful.

  Wataru · 1 · Nov 7 2014

• How do you find the x coordinates of the turning points of the function?
• How do you find the turning points of a cubic function?
• How many turning points can a cubic function have?
• How do you find the coordinates of the local extrema of the function?
• How do you find the local extrema of a function?
• How many local extrema can a cubic function have?
• How do I find the maximum and minimum values of the function `f(x) = x - 2 sin (x)` on the interval `[-pi/4, pi/2]`?
• If `f(x)=(x^2+36)/(2x), 1 <=x<=12`, at what point is f(x) at a minimum?
• How do you find the maximum of `f(x) = 2sin(x^2)`?
• How do you find a local minimum of a graph using the first derivative?
• How do you find the absolute minimum and maximum on `[-pi/2,pi/2]` of the function `f(x)=sinx^2`?
• How do you find the minimum values for `f(x)=2x^3-9x+5` for `x>=0`?
• How do you use the second derivative test to find all relative extrema of `f(x)=5+3x^2-x^3`?
• How do you find all relative extrema for `f(x) = 8/(x^2+2)`?
• How do you find all extrema in the interval [0, 2(pi)] for `y= sin x + cos x`?
• Given the function `y=2-x^2`, how do you determine the relative maximum or the relative minimum?
• How do you find absolute extrema of the function `g(x) = 2x + 5cosx` on the interval [0,2pi]?
• How do you find the extrema for `f(x)= (e^(10x))/(1+ e^(10x))` for [-5,5]?
• How do you find all local extrema/ relative maxima and minima for the function `y = x^3 - 3x^2 - 9x +15`?
• How do you find the extrema for `f(x)=x^4-18x^2+7`?
• How do you find the relative extrema for `f(x) =2x- 3x^(2/3) +2` on the interval [-1,3]?
• What is the absolute extrema of the function: `2x/(x^2 +1)` on closed interval [-2,2]?
• Find the absolute extrema of the given function `f(x)= sinx+cosx` on interval `[0,2pi]`?
• How do you find the extrema for `g(x) = sqrt(x^2 + 2x + 5)`?
• How duo you find all extrema in the interval `[0, 2pi]` if `y=x+sin x`?
• How do you find the extrema for `f(x) = x^2 +2x - 4` for [-1,1]?
• What are the absolute extrema of `y=cos^2 x - sin^2 x` on the interval [-2,2]?
• How do you find the coordinates of relative extrema `f(x)=x^3-4x^2+x+6`?
• How do you find all relative extrema of the function `f(x)= -x^3 -6x^2-9x-2`?
• How do you find all the extrema for `f(x) = x/(x^2+x+1)` on [-2,2]?
• How do you find all extrema for `f(x) = 2x + ln x`?
• How do you find the extrema for `f(x) = sec x` on the closed interval `[-pi/6, pi/3]`?
• How do you find the extrema of `f(x)=4 x^3-26 x^2+16x+1` on [0,3]?
• How do you find the relative extrema of the function `f (x) = x^3 + 6 x^2`?
• How do you find all relative extrema and points of inflection for the equation: `y=x^2 log_3x`?
• How do you find the relative extrema of the function `f (x)=x^4+4x^3+4x^2`?
• How do you locate the absolute extrema of the function `f(x)=x^3-12x` on the closed interval [0,4]?
• How would a horizontal line work in the Extreme Value Theorem?
• How do you find the global extreme values for `h(x)= x^2-3x` on [0,2]?
• How do you find the global extreme values for `V(x) = x(10 - 2x)( 16 - 2x)` on [0,5]?
• How do you find the global extreme values for `f(t) = tsqrt(4 - t²)` on [-1,2]?
• How do you find the global extreme values for `f(t) = 2cost + sin2t` on [0,pi/2]?
• How do you find the global extreme values for `y=x^2-6x-1` on [-2,2]?
• How do you find the absolute max and min for `f(x) = 5 + 2x` on [-2,1]?
• How do you find the absolute extrema of the function on the indicated interval by using the concept of the Extreme-Value Theorem f(x) = { |x| if -3 ≤ x ≤ 2 , 4-x if 2 < x ≤ 3 ; [ -3, 3]?
• What is the difference between Intermediate Value Theorem and the Extreme Value Theorem?
• What theorem guarantees the existence of an absolute maximum value and an absolute minimum value for f?
• How do use the first derivative test to determine the local extrema `f(x) = 3(x-4)^(2/3) +6`?
• How do use the first derivative test to determine the local extrema `f(x) = x^3 - x^2 - x + 3`?
• How do use the first derivative test to determine the local extrema `y = (x^2 + 2) /( x^2 + 1)`?
• How do use the first derivative test to determine the local extrema `(x)/[(x^2) +3]`?
• How do use the first derivative test to determine the local extrema `1/(x^2-x+2)`?
• How do use the first derivative test to determine the local extrema `(x^2-10x)^4`?
• How do use the first derivative test to determine the local extrema `x^2/(3(8-x))`?
• How do use the first derivative test to determine the local extrema `f(x)=x^4-4x^3+4x^2+6`?
• How do use the first derivative test to determine the local extrema `x^2-x-1`?
• How do use the first derivative test to determine the local extrema `y = sin x cos x`?
• How do use the first derivative test to determine the local extrema `f(x)=x-2tan(x)`?
• How do use the first derivative test to determine the local extrema `f(x)= -x^3 + 12x`?
• How do use the first derivative test to determine the local extrema `f(x)= x^3 - x^2 - 40x + 8`?
• How do use the first derivative test to determine the local extrema `f(x)= 4x^3 - 3x^4`?
• How do use the first derivative test to determine the local extrema `3-x^2`?
• How do use the first derivative test to determine the local extrema `x^2+1`?
• How do use the first derivative test to determine the local extrema `f(x) = x / (x^2+1)`?
• How do use the first derivative test to determine the local extrema `x^2-2x-3`?
• How do use the first derivative test to determine the local extrema `f(x) = (x+1)(x-3)^2`?
• How do use the first derivative test to determine the local extrema `f(x) = (x+3)(x-4)^2`?
• How do use the first derivative test to determine the local extrema `f(x) = x^3 + 6x^2`?
• How do use the first derivative test to determine the local extrema `f(x) = x³+3x²-9x+15`?
• How do use the first derivative test to determine the local extrema `f(x) = 3x^4-8x^3-90x^2+50`?
• How do use the first derivative test to determine the local extrema `f(x) = xsqrt(25-x^2)`?
• How do use the first derivative test to determine the local extrema `F(x) = -2x^3 - 9x^2 + 24x + 40`?
• How do use the first derivative test to determine the local extrema `f(x)=x^3-2x +pi`?
• How do use the first derivative test to determine the local extrema `y = x + sinx`?
• How do use the first derivative test to determine the local extrema `f(x)=x^3 - 9x^2 + 27x`?
• How do use the first derivative test to determine the local extrema `36x^2 +24x^2`?
• How do use the first derivative test to determine the local extrema `y=x(sqrt(8-x^2))`?
• How do use the first derivative test to determine the local extrema `f(x) = 3x^5 - 20x^3`?
• How do use the first derivative test to determine the local extrema `y= (x²-3x+3)/ (x-1)`?
• What are the extrema of `f(x)=-sinx-cosx` on the interval `[0,2pi]`?
• What are the extrema of `f(x)=-sin^2(ln(x^2))-cos^2(ln(x^2))` on the interval `[0,2pi]`?
• What are the local extrema of `f(x) = 2 x + 3 /x`?
• What are the local extrema of `f(x) = tan(x)/x^2+2x^3-x`?
• What are the local extrema of `f(x) = cos(x)/x^2+2x^3-x`?
• What are the local extrema of `f(x)= 5x - 3`?
• What are the local extrema of `f(x)= -x^3 + 3x^2 + 10x + 13`?
• What are the local extrema of `f(x)= 4^x` if they exist?
• What are the local extrema of `f(x)= sinx` on `[0,2pi]`?
• If `f'(x) = (x-8)^9 (x-4)^7 (x+3)^7`, what are the local minima and maxima of `f(x)`?
• What are the local maxima and minima of `f(x) = 4x^3 + 3x^2 - 6x + 1`?
• What are the local maxima and minima of `f(x)= (x^2)/(x-2)^2`?
• If you only have `f'(x)` is it possible to differentiate the local and global extrema of `f(x)`?
• What are the extrema and saddle points of `f(x, y) = xy+27/x+27/y`?
• What are the extrema and saddle points of `f(x, y) = x^2 + y^2 xy+27/x+27/y`?
• What are the extrema and saddle points of `f(x, y) = x^2 + y^2+27xy+9x+3y`?
• What are the extrema and saddle points of `f(x,y) = 2x^3 + xy^2 + 5x^2 + y^2`?
• What are the extrema and saddle points of `f(x,y) = 2x^(2) + (xy)^2 + 5x^2 - y/x`?
• What are the extrema of `f(x) = 5 + 9x^2 − 6x^3`?
• What are the extrema of `f(x) = (3x) / (x² - 1)`?
• What are the extrema and saddle points of `f(x,y) = xy + 1/x^3 + 1/y^2`?
• What are the extrema and saddle points of `f(x,y) = x^2y+y^3x -1/x^3 + 1/(xy^2)`?
• What are the extrema and saddle points of `f(x,y) = x^2y-y^2x`?
• What are extrema and saddle points of `f(x,y)=(x+y+1)^2/(x^2+y^2+1)`?
• What are the extrema of `f(x) = e^x(x^2+2x+1)`?
• What are the extrema of `f(x)=2x^3 + 5x^2 - 4x - 3`?
• What are extrema and saddle points of `f(x, y) = x^3y + 36x^2 - 8y`?
• What are the extrema of `h(x) = 7x^5 - 12x^3 + x`?
• Why is a point, b, an extremum of a function if `f'(b)=0`?
• What are the extrema of `f(x) = 1 - sqrt(x)`?
• What are the extrema of `f(x) = 64-x^2` on the interval `[-8,0]`?
• What are the extrema and saddle points of `f(x, y) = 6 sin x sin y` on the interval `x,y in[-pi,pi]` ?
• What are the extrema and saddle points of `f(x, y) = 6 sin(-x)* sin^2( y)` on the interval `x,y in[-pi,pi]` ?
• What are the extrema of `y=2x^3 - 5x^2 - 4x + 7`?
• What are the extrema of `f(x)=x^3-2x+5` on #[-2,2]?
• What are the extrema of `f(x) = 2 + (x + 1)^2` on #[-2,4]?
• What are the extrema of `f(x) = 7e^x`?
• What are the extrema and saddle points of `f(x, y) = xye^(-x^2-y^2)`?
• What are the extrema and saddle points of `f(x, y) = xy+e^(-x^2-y^2)`?
• What are the extrema and saddle points of `f(x, y) = xy(1-x-y)`?
• What are the extrema of `f(x) = x^3 - 27x`?
• What are the extrema of `f(x) = 8 - 2x` for `x>=6`?
• What are the extrema of `x^3-2x^2-8x`?
• What are the extrema of `y = x^4 - 3x^3 + 3x^2 - x`?
• What are the extrema and saddle points of `f(x,y) = e^y(y^2-x^2)`?
• What are the extrema and saddle points of `f(x,y) = xy(e^(y^2)-e^(x^2))`?
• What are the extrema and saddle points of `f(x,y) = x^2+xy+y^2+y`?
• What are the extrema and saddle points of `f(x)=2x^2 lnx`?
• What are the extrema of `f(x)=2x^3-3x^2-36x-3`?
• What are the extrema of `f(x)=2x+1`?
• What are the global and local extrema of `f(x)=x^3-3x+6` ?
• What are the global and local extrema of `f(x)=x^3+48/x` ?
• What are the extrema of `f(x)= x+sinx in [-pi,pi]` ?
• What are the global and local extrema of `f(x)=4x-x^2` ?
• What are the global and local extrema of `f(x) = x^3-9x+3` ?
• What are the global and local extrema of `f(x) = e^x(x^2+2x+1)` ?
• What are the global and local extrema of `f(x)=8x^3-4x^2+6` ?
• What are the global and local extrema of `f(x)=x^3-x^2-x` ?
• What are the global and local extrema of `f(x)=x^3-x^2-x+1` ?
• What are the global and local extrema of `f(x)=x^2 -2x +3` ?
• What are the local extrema an saddle points of `f(x,y) = x^2 + xy + y^2 + 3x -3y + 4`?
• What are the global and local extrema of `f(x)=x^3 + 4x^2 - 5x` ?
• What are the global and local extrema of `f(x)=2x^7-2x^5` ?
• What are the global and local extrema of `f(x) = x^2(2 - x)` ?
• What are the extrema of `f(x)=x/(x^2+9)` on the interval [0,5]?
• What are the extrema of `f(x)=x/(x-2)` on the interval [-5,5]?
• What are the extrema of `f(x)=(x^2 -9)^3 +10` on the interval [-1,3]?
• What are the extrema of `f(x)=1/x^3 +10x` on the interval [1,6]?
• What are the absolute extrema of `f(x)= |sin(x) + ln(x)|` on the interval (0 ,9]?
• What are the absolute extrema of `f(x)= |sin(x) - cos(x)|` on the interval [-pi,pi]?
• What are the absolute extrema of `f(x)= x/(x^2 + 25)` on the interval [0,9]?
• What are the absolute extrema of `f(x)= x^(2)+2/x` on the interval [1,4]?
• What are the absolute extrema of `f(x)= 2 + x^2 in [-2, 3]`?
• What are the absolute extrema of `f(x)= 2x^2 - x +5 in [-1, 5]`?
• What are the absolute extrema of `f(x)= cos(1/x)−xsin(1/x) in [-1/pi,1/pi]`?
• What are the absolute extrema of `f(x)= x^3 -3x+1 in [0,3]`?
• What are the absolute extrema of `f(x)= x^5 -x^3+x^2-7x in [0,7]`?
• What are the absolute extrema of `f(x)= xsqrt(25-x^2) in [-4,5]`?
• What are the absolute extrema of `f(x)= xsqrt(4-x^2) -x` in `[-1,2]`?
• What are the absolute extrema of `f(x)= x-ln(3x) in [1,e]`?
• What are the absolute extrema of `f(x)= xe^(x^2)/128in [-5,16]`?
• What are the absolute extrema of `f(x)= 6x^3 − 9x^2 − 36x + 3 in [-4,8]`?
• What are the absolute extrema of `f(x)= 3x^3 − sqrt(3x^2 − 6x + 3) in [-2,9]`?
• What are the absolute extrema of `f(x)=x/(x^2+1) in(0,2)`?
• What are the absolute extrema of `f(x)=(x-3)/(x^2+x-7) in(0,5)`?
• What are the absolute extrema of `f(x)=x-sqrt(5x-2) in(2,5)`?
• What are the absolute extrema of `f(x)=2x^2 - 8x + 6 in[0,4]`?
• What are the absolute extrema of `f(x)=(2x^3-x)/((x^2-64)` in `[-8,8]` ?
• What are the absolute extrema of `f(x)=(x^4) / (e^x) in[0,oo]`?
• What are the absolute extrema of `f(x)=(sinx) / (xe^x) in[ln5,ln30]`?
• What are the absolute extrema of `f(x)=(x^2 - 1)^3 in[-oo,oo]`?
• What are the absolute extrema of `f(x)=1/(1+x^2) in[oo,oo]`?
• What are the absolute extrema of `f(x)=(x-1)/(x^2+x+2) in[oo,oo]`?
• How do I find the absolute minimum and maximum of a function using its derivatives?
• What are the absolute extrema of `f(x)=x / (x^2 -6) in[3,7]`?
• What are the absolute extrema of `f(x)=sin2x + cos2x in[0,pi/4]`?
• What are the absolute extrema of `f(x)=2xsin^2x + xcos2x in[0,pi/4]`?
• What are the absolute extrema of `f(x)=x^(1/3)*(20-x)in[0,20]`?
• What are the absolute extrema of `f(x)=(x^3-7x^2+12x-6)/(x-1)in[1,4]`?
• What are the absolute extrema of `f(x)=x - e^x in[1,ln8]`?
• What are the absolute extrema of `f(x)=x / e^(x^2) in[1,oo]`?
• What are the absolute extrema of `f(x)=2x^3-15x^2 in[-2,10]`?
• What are the absolute extrema of `f(x)=9x^(1/3)-3x in[0,5]`?
• What are the absolute extrema of `f(x)=(9x^(1/3))/(3x^2-1) in[2,9]`?
• What are the absolute extrema of `f(x)=(x-2)(x-5)^3 + 12in[1,4]`?
• What are the absolute extrema of `f(x)=5x^7 - 7x^5 - 5 in[-oo,oo]`?
• What are the absolute extrema of `f(x)=(6x) / (4x+8) in[-oo,oo]`?
• What are the absolute extrema of `f(x)=8x^3 - 24x + 3 in[-oo,oo]`?
• What are the absolute extrema of `f(x)=(x+1)(x-8)^2+9 in[0,16]`?
• What are the absolute extrema of `f(x)=x^3 - 3x + 1 in[0,3]`?
• What are the absolute extrema of `f(x)=2cosx+sinx in[0,pi/2]`?
• What are the absolute extrema of `f(x) =x/(x^2-x+1) in[0,3]`?
• What are the absolute extrema of `f(x) =x^4 − 8x^2 − 12 in[-3,-1]`?
• What is the minimum value of `g(x) = x/csc(pi*x)` on the interval `[0,1]`?
• What is the minimum value of `g(x) = x^2+ 12x + 11?` on the interval `[-5,0]`?
• What is the minimum value of `g(x) = x^2-2x - 11/x?` on the interval `[1,7]`?
• What is the minimum value of `g(x) = (x-1)/(x^2+4)?` on the interval `[-2,2]`?
• What are the extrema of `g(x) = cos^2x+sin^2x?` on the interval `[-pi,pi`?
• What are the extrema of `g(x) = 5x-80?` on the interval `[-1,10]`?
• What are the extrema of `f(x)=3x-1/sinx` on `[pi/2,(3pi)/4]`?
• What are the extrema of `f(x)=-8x^2+x` on `[-4,8]`?
• What are the extrema of `f(x)=x^2+2x+15` on `[-oo,oo]`?
• What are the extrema of `f(x)=5x^2+4x-3` on `[-oo,oo]`?
• What are the extrema of `f(x)=-2x^2+4x-3` on `[-oo,oo]`?
• What are the extrema of `f(x)=3x^2 - 12x + 13` on `[-oo,oo]`?
• What are the extrema of `f(x)=-3x^2+30x-74` on `[-oo,oo]`?
• What is the absolute minimum of `f(x)=xlnx`?
• What are the extrema of `f(x)=x^2 - 8x + 12` on `[-2,4]`?
• What are the extrema of `f(x)=(x - 4)(x - 5)` on `[4,5]`?
• What are the extrema of `f(x) = e^(-x^2)` on `[-.5, a]`, where `a > 1`?
• What are the extrema of `f(x)=4x^2-24x+1`?
• What are the extrema of `f(x)=f(x)= -x^2+8x+7`?
• What are the extrema of `f(x)=f(x)= x^2 -4x +3`?
• What are the extrema of `f(x)=3+ 2x -x^2`?
• What are the extrema of `f(x)=-x^2 +5x -1`?
• What are the extrema of `f(x)=x^2-192x+8` on `x in[-4,9]`?
• What are the extrema of `f(x)=(x^2)/(x^2-3x)+8` on `x in[4,9]`?
• What are the extrema of `f(x)=x^2 - 6x + 11` on `x in[1,6]`?
• What is the minimum value of `f(x)=3x^2-6x+12`?
• What are the extrema of `f(x) = 3x^2 + 12x + 16`?
• What are the extrema of `g(x) = 2 sin(2x - pi) + 4` on `[-pi/2,pi/2]`?
• What are the local extema of `f(x)=x^2-4x-5`?
• What are the local extrema of `f(x)=(x-3)(x^2-2x-5)`?
• What are the local extrema of `f(x)=(x-1)/(x-4)`?
• What are the local extrema of `f(x)=x^2/lnx`?
• What are the local extrema of `f(x)= x^2/(x^2-3x-5)`?
• What are the local extrema of `f(x)= xe^-x`?
• What are the local extrema of `f(x)= e^(x^2)-x^2e^x`?
• What are the local extrema of `f(x)= x^3-7x`?
• What are the local extrema of `f(x)= (x^5-x^2-4)/(x^3-3x+4)`?
• What are the local extrema of `f(x)= x/((x-2)(x-4)^3)`?
• What are the local extrema of `f(x)= ((x-2)(x-4)^3)/(x^2-2)`?
• What are the local extrema of `f(x)= xsqrt(x+3/x)`?
• What are the local extrema of `f(x)= 1/sqrt(x^2+e^x)-xe^x`?
• What are the local extrema of `f(x)= lnx/e^x`?
• What are the local extrema of `f(x)= e^xln1^x`?
• What are the local extrema of `f(x)= xlnx-xe^x`?
• What are the local extrema of `f(x)= 1/x-1/x^3+x^5-x`?
• What are the local extrema of `f(x)= (x^3-x^2-5x+4)/(x-2)^2`?
• What are the local extrema of `f(x)= (3x^3-2x^2-2x+43)/(x-1)^2+x^2`?
• What are the local extrema of `f(x)= x^3-x+3/x`?
• What are the local extrema of `f(x)= 4x^2-2x+x/(x-1/4)`?
• What are the local extrema of `f(x)= x^2(x+2)`?
• What are the local extrema of `f(x)= x^3-3x^2-9x+7`?
• What are the local extrema of `f(x)= -2x^2 + 9x`?
• What are the local extrema of `f(x)= x^3 - 3x^2 - x + 1`?
• What are the local extrema of `f(x)= x^3 - 9x^2 + 19x - 3`?
• What are the local extrema of `f(x)= x^3-6x^2+15`, if any?
• What are the local extrema, if any, of `f(x)= 4x+6/x`?
• What are the local extrema, if any, of `f(x)= (4x-3)^2-(x-4)/x`?
• What are the local extrema, if any, of `f(x)= 2x+15x^(2/15)`?
• What are the local extrema, if any, of `f(x)= x^2-1`?
• What are the local extrema, if any, of `f(x)= 2x^3 – 6x^2 – 48x + 24`?
• What are the local extrema, if any, of `f(x)= –2x^3 + 6x^2 + 18x –18`?
• What are the local extrema, if any, of `f(x)= (x^2 + 6x-3)*e^x + 8x –8`?
• What are the local extrema, if any, of `f(x)= 120x^5 - 200x^3`?
• What are the local extrema, if any, of `f (x) = x^3 - 6x^2 - 15x + 11`?
• What are the local extrema, if any, of `f (x) = x^4-8x^2-48`?
• What are the local extrema, if any, of `f (x) = x^3-12x+2`?
• What are the local extrema, if any, of `f (x) = 2x^4-36x^2+5`?
• What are the local extrema, if any, of `f (x) =2ln(x^2+3)-x`?
• What are the local extrema, if any, of `f (x) =x^3-3x+6`?
• What are the local extrema, if any, of `f (x) =(x^3-3)/(x+6)`?
• What are the local extrema, if any, of `f (x) =x^3+3x^2-5x`?
• What are the local extrema, if any, of `f (x) =(x^3+3x^2)/(x^2-5x)`?
• What are the local extrema, if any, of `f (x) =xe^(x^3-7x)`?
• What are the local extrema, if any, of `f (x) =x^2-2x+4`?
• What are the local extrema, if any, of `f (x) =(x^2-2x)^3+(4x^2-3x^4)*e^(2x)`?
• What are the local extrema, if any, of `f (x) =x/(-12x+2`?
• What are the local extrema, if any, of `f (x) =(x+1)^7/2`?
• What are the local extrema, if any, of `f (x) =(x^3−4 x^2-3)/(8x−4)`?
• What are the local extrema, if any, of `f (x) =a(x-2)(x-3)(x-b)`, where `a` and `b` are integers?
• What are the local extrema, if any, of `f (x) =(lnx)^2/x`?
• What are the local extrema, if any, of `f (x) =(xlnx)^2/x`?
• What are the local extrema, if any, of `f (x) =(x^3 + 2x^2)/(3 - 5x)`?
• What are the local extrema, if any, of `f (x) =sqrt(4-x^2)`?
• What are the local extrema, if any, of `f (x) =80+108x-x^3`?
• What are the local extrema of `f(x) = x^3 - 3x^2 - 9x +1`?
• What are the local extrema, if any, of `f(x) =x^2 + 9x +1`?
• What are the local extrema, if any, of `f(x) =x^2(x+2)`?
• What are the local extrema, if any, of `f(x) =2x^3 -3x^2+7x-2`?
• What are the local extrema, if any, of `f(x) =(lnx-1)^2 / x`?
• What are the local extrema, if any, of `f(x) =2-x^2`?
• How do you find the relative extrema for `f(x)=(9x^(2)+1)/x`?
• How do you find the relative extrema for `y=x^3`?
• How do you find local maximum value of f using the first and second derivative tests: `f(x)= sinx`?
• What is the relative minimum, relative maximum, and points of inflection of `f(x) = x^4 - 4x^2`?
• How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `f(x)=-x^2+6x+6`?
• What is the relative maximum of y = csc (x)?
• How do you find the exact relative maximum and minimum of the polynomial function of `g(x) = x^3 - 3x^2 - 9x +1`?
• How do you find the local extremas for `f(x)=xe^x`?
• How do you find the local extremas for `f(x)= (x-3)^3`?
• How do you find the local extremas for `g(x) = x^2 + 1`?
• How do you find the local extremas for `g(x) = - |x+6|`?
• How do you find the local extrema for `f(x) = 3x^5 - 10x^3 - 1` on the interval [-1,1]?
• How do you find the local extrema for `y=4x^3 + 7`?
• How do you find the local extremas for `x(x-1)` on [0,1]?
• How do you find the local extremas for `f(x)=2x + (5/x)`?
• How do you find the local extremas for `f(x)=x^(1/3)(x+8)`?
• How do you find the local extrema for `f(x) = (3x + 4)^(-3/4)`?
• How do you find the local extrema for `f(x)=5x-x^2`?
• How do you find the local extrema for `(x^2)(e^-x)` from [-2,4]?
• How do you find the local extrema for `y=sqrtx/(x-5)`?
• How do you find the local extrema for `f(x) = 2-2x^2` on domain `-1 <= x <= 1`?
• How do you find the local extrema for `y = [1 / x] - [1 / (x - 1)]`?
• How do you find the local extrema for `f(x)=-0.12x^3 + 900x - 830`?
• How do you find the local extrema for `(e^x)(x^2)`?
• How do you find the local extrema for `f(x) = x sqrt( x - 3 )`?
• How do you find the local extrema for `f(x) = x - ln(x)` on [0.1,4]?
• How do you find the local extrema for `f(x) = (x-3)^3` on (-∞, ∞)?
• How do you find the local extrema for `f(x)= x^4-4x³`?
• How do you find the local extrema for `f(x)=(x-3)(x-1)(x+2)`?
• How do you find the local extrema for `f(x) = 2x^3 - x^2 - 4x +3`?
• How do you find the local extrema for `F(x)= sin (x + (π/2) )`?
• Question #4a6db
• How do you find the absolute extreme values of each function on the interval `y = 10 - 8x^2` on [-1,2]?
• How to find the max and minimum of `f(x)= abs(x-1 )+ 2abs(x+5) + 3abs(x-4)` using derivatives?
• How do you find the local extrema of `f(x)=x^3-6x`?
• How do you find the local extrema of `g(x)=-x^4+2x^2`?
• Question #31214
• What is the derivative of `y = ln(cscx)`?
• Question #64b09
• Calculus 1 absolute minimum and maximum of a function?
• What is the maximum value of `(3-cosx)/(1+cosx)` for `0< x < (2pi)`?
• Given `f(x) = -2(x+2)(x-1)^2` on the open interval (-3,3). How do you determine the x coordinate of the relative minimum of f (x) in the open interval (-3,3)?
• Question #115fc
• A differentiable function `f` has only one critical number: `x=-3`. Identify the relative extrema of `f` at (-3, f(-3)) if `f'(-4)=(1/2)` and `f'(-2)=-1`?
• Does the function `f(x)= -x^2+6x-1` have a minimum or maximum value?
• What is the minimum of `f(x)=|x-1|+|x-2|+cdots+|x-1391|` function?
• Find the absolute maximum and absolute minimum values of `f(x) = x^(1/3) e^(−x^2/8)` on the interval [−1, 4]?
• Question #a681a
• Question #eb2b6
• Question #cf6e2
• What is the difference between 'relative maximum(or minimum)' and 'absolute maximum(or minimum)' in functions?
• Question #3d707
• The graph of `y=ax^2+bx` has an extremum at `(1,-2)`. Find the values of a and b?
• Can someone help me with this question ? i cant find the derivatives or the others !! someone help me please ?