Q85 / 150 · MHT CET 2026 (13 April Shift 2) · Mathematics

Let $f(x)$ be the differentiable function for all $x$ such that $f'(x) \leq 5$ and $f(1) = 4$. The maximum value of $f(5)$ is...

  • A
    $16$
  • B
    $20$
  • Correct answer
    C
    $24$
  • D
    $25$

Solution

By Lagrange's Mean Value Theorem on the interval $[1, 5]$, there exists some $c \in (1, 5)$ such that

$f'(c) = \dfrac{f(5) - f(1)}{5 - 1}$

Given that $f'(x) \leq 5$ for all $x$, we have $f'(c) \leq 5$.

$\dfrac{f(5) - 4}{4} \leq 5$

$f(5) - 4 \leq 20$

$f(5) \leq 24$

The maximum value of $f(5)$ is $24$.

Answer: $24$

Hence, the correct answer is option: 'C'.

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