Mathematics - Continuity - Differentiability Question with Solution | TestHub

$\therefore \mathrm{a}\left|{\sin }^7\mathrm{x}\right|$ is differentiable at $\mathrm{x}=0$ and its d.e. is 0 for all $\mathrm{a}\in \mathrm{R}$ and $\mathrm{c}|\mathrm{x}{|}^5$ is differentiable at $x=0$ and its d.e. is 0 for all $c\in R$.

But at $x=0$, L.H. derivative of $b{e}^{|x|}=-b$ and R.H. derivative $=b$

∴ for ${\mathrm{be}}^{\mathrm{x}\mid }$ to be differentiable at $\mathrm{x}=0,\mathrm{b}=-\mathrm{b}$ $\Rightarrow \mathrm{b}=0$