Question

The set of all points where the function f(x) = x$\left\lbrack \frac{x^{2}}{a} \right\rbrack$ is differentiable is

• A. (–∞, ∞)
• B. (–∞, 0) ∪ (0, ∞)
• C. (0, ∞)
• D. [0, ∞]

Answer 1

Answer: (A)

(–∞, ∞)

Answer 2

f(x) = x =

f′(x) = $\left\{ \begin{array} { l l } 2 x & \text { if } x > 0 \\ - 2 x & \text { if } x < 0 \end{array} \right.$

f(x) is differentiable for all x ∈ R except possibly at x = 0.

But f′(0⁺) = $f ^ { \prime }$ (0^–) = 0.

Hence f is differentiable every where