Answer
Every $c \in(a, b)$ is the $c$ that satisfies the conclusion of the MVT.
Work Step by Step
Consider the linear function
$$ f(x)= mx+l$$
By using MVT on the interval $[a, b]$, we have
\begin{align*}
f^{\prime}(c)&=\frac{f(b)-f(a)}{b-a}\\
&=\frac{(m b+l)-(m a+l)}{b-a}\\
&=\frac{m(b-a)}{b-a}=m
\end{align*}
On the other hand
$$f'(x)= m\ \ \ \text{for any }\ x $$
Then every $c \in(a, b)$ is the $c$ that satisfies the conclusion of the MVT.
