QuestionConsider the function $f(x)=x^{2 / 5}(x-5)$. This function has two critical numbers $A<B$
Then $A=$ $\square$ and $B$ $\square$ .
For each of the following intervals, tell whether $f(x)$ is increasing or decreasing. $$\begin{array}{ll} (-\infty, A]: ? & ? \\ {[A, B]: ?} & \vee \\ {[B, \infty)} & ? \end{array}$$
The critical number $A$ is ? $\square$ and the critical number $B$ is $\square$ ? $\square$ There are two numbers $C<D$ where either $f^{\prime \prime}(x)=0$ or $f^{\prime \prime}(x)$ is undefined.
Then $C=$ $\square$ and $D=$ $\square$ Finally for each of the following intervals, tell whether $f(x)$ is concave up or concave down. $(-\infty, C)$ : ? $(C, D)$ ? $\square$ $(D, \infty)$ $?$ $\square$