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

Then $A =$ and $B$ .

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

The critical number $A$ is and the critical number $B$ is
There are two numbers $C 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.
$(-\infty, C)$:
$(C,D)$
$(D,\infty)$