Hey guys so I need help on two questions that I'm sort of stuck on.

1. Find the critical numbers of the given function: f(x) = 2x^{3}+x^{2}+2x

So I got f'(x) = 6x^{2}+2x+2

Factored out the 2(3x^{2}+x+1)

I can't factor this out anymore, so is the answer there are no critical numbers?

2. Find the absolute max and min values of f on the given interval.

√ = square root

f(t) =^{3}√t * (8-t), [0,8]

So I used product rule on this one and got

f'(t) = 3/2√t * (8-t) -^{3}√t = 0

3(8-t)-3√t = 0

So, I'm uncertain about the critical numbers here as well are they 8 and 0?