Answer the Problem $f ( x ) = ( x - 1 ) ^ { 2 / 3 }$

Essay

Answer the problem.
-Let $f ( x ) = ( x - 1 ) ^ { 2 / 3 }$
(a) Does $f ^ { \prime } ( 1 )$ exist?
(b) Show that the only local extreme value of $f$ occurs at $x = 1$ .
(c) Does the result of (b) contradict the Extreme Value Theorem?
(d) Repeat parts (a) and (b) for $f ( x ) = ( x - c ) ^ { 2 / 3 }$ .
Give reasons for your answers.