Question

Discuss applicability of Rolle's Theorem for x + |x| in interval [-1, 1]

• A. Not continous and differentiable
• B. Continous and non-differentiable
• C. Not continous and not differentiable
• D. Continous and differentiable

Answer 1

The correct option is B

Continous and non-differentiable

Let f(x) = x + |x|

Then, f'(x) = 0 at x < 0

And f'(x) = 2 at x > 0

So, it is not differentiable.

But as x and |x| are continuous functions so their sum is also continuous.