Question

Can the mean value theorem be applied?

Answer 1

Mean value theorem can be applied to the function $f\left(x\right)$ if it is continuous at a closed interval $[a,b]$ and differentiable at open interval $(a,b)$, with at least one value $c$ in between the interval $(a,b)$.

$f’\left(c\right)=\frac{\mathrm{f}\left(\mathrm{b}\right)-\mathrm{f}\left(\mathrm{a}\right)}{\mathrm{b}-\mathrm{a}}$

Hence, mean value theorem can be applied.