Question

If f(x) = ||x| − 1|, then points, where f(x) is not differentiable, is/are ______.

Options

• 0, 1

• ± 1, 0

• 0

• 1 only

Answer 1

If f(x) = ||x| − 1|, then points, where f(x) is not differentiable, are ± 1, 0.

Explanation:

Using a graphical transformation:

Since the function is known to be non-differentiable at sharp edges, figure (iii), y = || x | − 1|, has three sharp edges at x = −1, 0, and 1.

Thus, f (x) cannot be differentiated at {0, ±1}.