1) Find the Critical Numbers for$\displaystyle h(p) = \frac{p - 1}{p^2+4}$

$\displaystyle h'(p) = \frac{p^2 + 4 - (p - 1)(2p)}{(p^2 + 4)^2}$

after all the work is done I get

$\displaystyle -p^2 + 2p + 4 = 0$

There aren't any critical numbers is what I got but I'm not sure.

2) Find the Critical Numbers for$\displaystyle g(x) = \sqrt{1 - x^2} $

$\displaystyle g'(x) = \frac{2x}{2 \sqrt{1-x^2}}$

$\displaystyle \frac{x}{\sqrt{1-x^2}} = 0$

I get $\displaystyle x = 0$ as a critical number but I'm not sure if it's right or the only answer

3) Find the Absolute max and min for

$\displaystyle f(t) = 2cos(t) + sin(2t)$ in the interval $\displaystyle [0 , \frac{pi}{2}]$

after simplifying the derivative for it I get:

$\displaystyle f'(t) = 2(cost(2t) + sin(t))$

I don't know what to do with it since I am bad with trig functions in these types of problems.