How do you find the critical numbers of  f(t)=t(4-t)^(1/2)?

Nov 9, 2017

Domain of $f$ is $\left(- \infty , 4\right]$
$f ' \left(t\right) = \frac{8 - 3 t}{2 \sqrt{4 - t}}$
$f ' \left(t\right) = 0$ at $t = \frac{8}{3}$ and $f ' \left(t\right)$ does not exist at $x = 4$.
Both numbers are in the domain of $f$, so both are critical numbers for $f$.