Question

Let f : R → R be a function defined by f(x) = max {x, x³}. The set of all points where f(x) is NOT differentiable is

• A. {−1, 1}
• B. {−1, 0}
• C. {0, 1}
• D. {−1, 0, 1}

Answer 1

Answer: (D)

{−1, 0, 1}

Answer 2

f(x) = max. {x , x³}

= $\left{ \begin{matrix} \begin{matrix} x; \ x^{3}; \end{matrix} \ x; \ x^{3} \end{matrix} \right.\ \begin{matrix} \begin{matrix} x < - 1 \

• 1 \leq x \leq 0 \end{matrix} \ 0 < x < 1 \ x \geq 1 \end{matrix}$

∴ f’(x) = $\left{ \begin{matrix} \begin{matrix} 1; \ 3x^{2}; \end{matrix} \ 1; \ 3x^{2} \end{matrix} \right.\ \begin{matrix} \begin{matrix} x < - 1 \

• 1 \leq x \leq 0 \end{matrix} \ 0 < x < 1 \ x \geq 1 \end{matrix}$ Clearly f is not differentiable at -1, 0 and 1.

∴ ‘D’ is the correct alternative.