Mathematics - Continuity - Differentiability Question with Solution | TestHub

Since$f\left(x\right) \ge 1 \forall x \in \left[a, b\right]$for$g\left(x\right)$
LHD at$x=a$is zero
And RHD at$\left(x=a\right)= \underset{x\to a^{+}}{\lim }\frac{\underset{a}{\overset{x}{\int }}f\left(t\right)dt-0}{x-a}= \underset{x\to a^{+}}{\lim }f\left(x\right) \ge 1$
Hence$g\left(x\right)$is not differentiable at$x=a$
Similarly LHD at$x=b$is greater than 1
$g\left(x\right)$is not differentiable at$x=b$