Question

help: This one is bugging the hell out of me :)

For f(x)=2x^3+3x^2-36x
(a) find the intervals on which f is increasing or decreasing
(b) find the local maximum and minimum values of f
(c) find the intervals of concavity and the inflection points

Answer 1

\[f'(x)=6x^2+6x-36=6(x^2+x-6)=6(x+3)(x-2)\] zeros of the derivative (critical points) are -3 and 2 so it will be increasing on
\[(-\infty, -3)\cup (2,\infty)\] and decreasing on
\[(-3,2)\]

Answer 2

-3 gives a local max, 2 gives a local min, and you and find concavity by the second derivative which is
\[f''(x)=12x+6\] which is 0 at
\[x=-\frac{1}{2}\]

Answer 3

Thanks satellite73