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According to the Mean Value Theorem, if a function $f$ is differentiable on $(a,b)$ and continuous on $[a,b]$, then there exists a number $c$ in $(a,b)$ such that:

A

$f\left( a \right) =f\left( b \right)$

B

$f^{ \prime }\left( c \right) =0$

C

$f^{ \prime }\left( c \right) =f\left( a \right) -f\left( b \right)$

D

$f^{ \prime }\left( c \right) =\cfrac { f\left( b \right) -f\left( a \right) }{ b-a }$

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