Allied & ICAR Exam Bank • ALLIED_0042 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

According to the Mean Value Theorem, if $f(x) = x^2$ on $[1, 3]$, the point $c \in (1, 3)$ where $f'(c) = \frac{f(3) - f(1)}{3 - 1}$ is:

Options:

  • (A) $2$
  • (B) $1.5$
  • (C) $2.5$
  • (D) $\sqrt{3}$

Answer Key:

A

Step-by-Step Solution & Explanation

$\frac{f(3) - f(1)}{3 - 1} = \frac{9 - 1}{2} = 4$. $f'(c) = 2c = 4 \implies c = 2$.
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