Allied & ICAR Exam Bank • ALLIED_0039 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

If $f(x) = |x|$, at $x = 0$ the function is:

Options:

  • (A) Continuous but not differentiable
  • (B) Differentiable and continuous
  • (C) Neither continuous nor differentiable
  • (D) Discontinuous

Answer Key:

A

Step-by-Step Solution & Explanation

$f(x)$ is continuous everywhere, but the left derivative is $-1$ and right derivative is $+1$ at $x = 0$, so it is not differentiable at $x = 0$.
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