Consider the function $f(x)$ whose derivative is graphed below.

a$)$ Where are the critical points of $f?$

Critical points at $x=$

b$)$ Where are the inflection points of $f?$ Label them on the graph.

Inflection points at $x=6$

$$

c$)$ You may assume that $f(0)=-3.$ Identify the maximum and minimum of $f$ on the interval $0,12.$

Maximum: $$

Minimum: $$