Q75 / 155 · WBJEE 2025 · Mathematics

Let $f$ be a function which is differentiable for all real $x$. If $f(2)=-4$ and $f^{\prime}(x) \geq 6$ for all $x \in[2,4]$

A
$f(4) \lt 8$
B
$f(4) \geq 12$
Correct answer
C
$f(4) \geq 8$
D
$f(4) \lt 12$

Solution

By LMVT $f^{\prime}(x)=\frac{f(4)-f(2)}{4-2}$ as $f^{\prime}(x) \geq 6 \Rightarrow f(4) \geq 8$

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

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