Consider the function , then

Maths Functions, Limits, Continuity and Differentiability NTA Abhiyas Question - Continuity and Differentiability Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

f (x) is continuous and differentiable at x = 4

f (x) is continuous but non differentiable at x = 4

f (x) is discontinuous but differentiable at x = 4

f (x) is discontinuous and non- differentiable at x = 4

Text Solution

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The correct answer is:

f (x) is continuous but non differentiable at x = 4

Let us shift the graph off (x) in the direction of the negative x- axis by 4 units & let g (x) - f (x + 4)

g (x) at x = 0 will have the same behavior as off (x) at x = 4

Continuity at x = 0,

is continuous at x = 0

f (x) is continuous at x = 4

Differentiability at x = 0

Clearly,

g (x) is non-differentiable at x = 0

f (x) is non-differentiable at x = 4

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