Question

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

Answer 1

Please see below.

Explanation:

Domain of `f` is `(-oo,4]`

`f'(t) = (8-3t)/(2sqrt(4-t))`

`f'(t) = 0` at `t=8/3` and `f'(t)` does not exist at `x=4`.

Both numbers are in the domain of `f`, so both are critical numbers for `f`.