Consider the function $f(x) = x^{1/5}(x- 7)$. This function has two critical numbers $A<B$

Then $A =$ and $B$ .

Hint:

For each of the following intervals, tell whether $f(x)$ is increasing or decreasing.
$(-\infty, A]$: ? increasing decreasing
$[A,B]$: ? increasing decreasing
$[B,\infty)$ ? increasing decreasing

The critical number $A$ is ? a relative maximum a relative minimum neither max nor min and the critical number $B$ is ? a relative maximum a relative minimum neither max nor min
There are two numbers $C<D$ where either $f''(x)=0$ or $f''(x)$ is undefined.

Then $C =$ and $D =$ .

Finally for each of the following intervals, tell whether $f(x)$ is concave up or concave down.
$(-\infty, C)$: ? concave up concave down
$(C,D)$ ? concave up concave down
$(D,\infty)$ ? concave up concave down