Find the Value or Values Of $c$ That Satisfy the Equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$

Essay

Find the value or values of $c$ that satisfy the equation $\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )$ in the conclusion of the Mean Value Theorem for the function and interval.
-Let $f ( x ) = \left| x ^ { 3 } - 9 x \right|$
(a) Does $f ^ { \prime } ( 0 )$ exist?
(b) Does $f ^ { \prime } ( 3 )$ exist?
(c) Does $f ^ { \prime } ( - 3 )$ exist?
(d) Determine all extrema of $f$ .