# Using the second derivative test, how do you find the local maximum and local minimum for #f(x) = x^(3) - 6x^(2) + 5#?

##### 1 Answer

Apr 16, 2015

Maxima at x=0, Minima at x=4

Start finding the critical points by equating f '(x)=0

f '(x)=

Critical points would be known by solving

To apply the second derivative test, find the second derivative f"(x) = 6x-12.

For x=0, f"(x) = -12 (<0), hence it would be a maxima and for x=4, f"(x)=24-12= 12 (>0), it would be a minima.