`Let h(x) = min.{x, x 2 } for every real number x. Then:

Maths Differentiation and Applications of Derivatives General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

h is continuous for all x

h is differentiable for all x

h ′ (x) = 1, for all x > 1

h is not differentiable at two values of x

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a, c and d)

= h(x) =

Thus h is differentiable except possibly at x = 0,

1h ′ (0 + ) =

= = 0

h ′ (0 – ) =

= = 1

Hence h is not differentiable at x = 0. Similarly h ′ (1 + ) =1 and h ′ (1–) = 2. Also h(x) = 0 = h(0) = h(x) and h(x) = 1 = h(1) = h(x).

Hence h is a continuous function and is not differentiable at two values of x.

Conclusions can also be made by drawing graph of the

function h(x).

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