Allied & ICAR Exam Bank • ALLIED_2637 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The function $f(x) = |x - 2|$ at $x = 2$ is:

Options:

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

Answer Key:

A

Step-by-Step Solution & Explanation

$f(x)$ is continuous everywhere including $x = 2$. However, left derivative is $-1$ and right derivative is $+1$, so it is not differentiable at $x = 2$.
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