Q. Let $f$ be continuous on [1, 5] and differentiable in (1, 5). If $f(1) = - 3$ and $f^{'}(x) \geq 9$ for all $x \in (1,\ 5)$, then
A) $f(5) \geq 33$
B) $f(5) \geq 36$
C) $f(5) \leq 36$
D) $f(5) \geq 9$
Explanation
(a)
By Mean value theorem
$f^{'}(x) = \frac{f(5) - f(1)}{5 - 1} \geq 9$
$\Rightarrow \frac{f(5) + 3}{4} \geq 9 \Rightarrow f(5) \geq 33$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.