SOLUTION: Locate the critical points of the following function. Then use the second derivative test to determine whether they correspond to local maxima, local minima, or neither. f(x)=-x^3

Question 1155434: Locate the critical points of the following function. Then use the second derivative test to determine whether they correspond to local maxima, local minima, or neither.
f(x)=-x^3 -9x^2
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
f(x)=-x^3-9x^2
f'(x)=-3x^2-18x
set equal to 0
3x^2-18x=0
3x^2+18x=0
3x(x+6)=0
0 and -6 are the critical points
f''(x)=-6x-18
when x=0 f''(x) is -18, so that is a maximum, local
when x=-6, f''(x)=18, so that is a minimum, local

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