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 $f ( x ) = ( x - 7 ) ^ { 2 / 3 }$
(a) Does $f ^ { \prime } ( 7 )$ exist?
(b) Show that the only local extreme value of $f$ occurs at $x = 7$.
(c) Does the result of (b) contradict the Extreme Value Theorem?
(d) Repeat parts (a) and (b) for $\mathrm { f } ( \mathrm { x } ) = ( \mathrm { x } - \mathrm { c } ) ^ { 2 / 3 }$.
Give reasons for your answers.

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The Answer of  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 $f ( x ) = ( x - 7 ) ^ { 2 / 3 }$
(a) Does $f ^ { \prime } ( 7 )$ exist?
(b) Show that the only local extreme value of $f$ occurs at $x = 7$.
(c) Does the result of (b) contradict the Extreme Value Theorem?
(d) Repeat parts (a) and (b) for $\mathrm { f } ( \mathrm { x } ) = ( \mathrm { x } - \mathrm { c } ) ^ { 2 / 3 }$.
Give reasons for your answers.

Find the Value or Values Of ccc That Satisfy the Equation f(b)−f(a)b−a=f′(c)\frac { f ( b ) - f ( a ) } { b - a } = f ^ { \prime } ( c )b−af(b)−f(a)​=f′(c)

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