Determine where f(x)=8x^{3}+18x^{2}-24x-9 has any local maximum or local minimum values.

What I did:

f'(x)=24x^{2}+36x-24

0=24x^{2}+36x-24

0=12(x+2)(2x-1)

x=-2, (1/2)

After getting the critical numbers, I'm not really sure where to go on from there because of the answers given.

Can someone explain to me about finding local max and min a bit.

From the multiple choice answers that were given, it was either

a. local max at x=3/4, local min at x=-4/3

b. local max at x=-3/4, local min at x=4/3

c. local max at x=4/3, local x=-3/4

d. local max at x=-4/3, local min at x=3/4