How do you find the maxima and minima of the function #f(x)=x^3+3x^2-24x+3#?
1 Answer
Jan 30, 2017
maxima at
#(-4,83)#
minima at#(2,-25)#
Explanation:
We have:
# f'(x) = 3x^2+6x-24 #
At a max/min (turning point)
# :. \ \ \ \ x^2+2x-8=0 #
# :. (x-2)(x+4) = 0#
# :. x=-4,2,#
When
When
To determine the nature of the turning points we look at the second derivative. Differentiating again wrt
# f''(x) = 6x+6 #
When
When
So the maxima and minima are:
maxima at
#(-4,83)#
minima at#(2,-25)#
We can confirm these results graphically:
graph{x^3+3x^2-24x+3 [-10, 10, -50, 100.]}