Question

Which of the following function is not differentiable at exactly two points of its domain-

• A. $f\left(x\right)$
• B. $g\left(x\right)$
• C. $k\left(x\right)$
• D. None of these

Answer 1

Answer: (B)

$g\left(x\right)$

$f^{\prime }\left(x\right)=\{\begin{array}{c}2(1-1)=0ifx<1\\ 0,ifx\in [1,3]\\ -2(x-1)=-4ifx<3\end{array}$
$g^{\prime }\left(x\right)=\{\begin{array}{c}\frac{-1}{2\sqrt{-x}}\to \infty ifx<0\\ 1ifx\in [0,4]\\ 3ifx\in (4,\infty )\end{array}$
$h^{\prime }\left(x\right)=\{\begin{array}{c}a{e}^{x}ifx<0\\ 1ifx\in [0,3]\\ \frac{1}{3}ifx>3\end{array}$
Hence, g(x) has two points as non differentiable.