Increasing$/$Decreasing and Concavity Let $f(x)=\sqrt[3]{27x-x^3}$

$($a$)$ Find the critical points of $f(x).$

$($b$)$ Find the intervals where $f(x)$ is increasing and decreasing.

$($c$)$ Using the graph below, where is $f(x)$ concave up and down. You may round your answer to the nearest $10$th$.$