Mathematics - Continuity - Differentiability Question with Solution | TestHub

We have $f(x)=[3x]+14+|(2x+1)(2x-1)|(2x-1)(x+2)+\sin \left(\frac{\pi x}{2}\right)$

For $\mathrm{x}\in [-4,4]$

$-12\le 3\mathrm{x}\le 12$

$\therefore x=\underset{25\text{ points }}{\underbrace{\frac{-12}{3},\frac{-11}{3},\frac{-10}{3},\dots \dots ,\frac{-1}{3},0,\frac{1}{3},\dots \dots ,\frac{11}{3},\frac{12}{3}}}$

But $f(-4)=f\left(-4^{+}\right)$

$\Rightarrow \mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=-4$.

Here, $f(x)$ is continuous at $x=\frac{-1}{2}$ but non - derivable at $x=\frac{-1}{2}$.

As discontinuing ⇒ non - differentiability

So, $f(x)$ is non - derivable at 25 points in $[-4,4]$