JEE PYQ: Application Of Derivatives Question 34
Question 34 - 2020 (04 Sep Shift 1)
Let $f$ be a twice differentiable function on $(1, 6)$. If $f(2) = 8$, $f’(2) = 5$, $f’(x) \ge 1$ and $f’’(x) \ge 4$ for all $x \in (1, 6)$, then:
(1) $f(5) + f’(5) \le 26$
(2) $f(5) + f’(5) \ge 28$
(3) $f’(5) + f’’(5) \le 20$
(4) $f(5) \le 10$
Show Answer
Answer: (2)
Solution
By LMVT: $\frac{f(5) - f(2)}{3} \ge 1 \Rightarrow f(5) \ge 11$. Also $\frac{f’(5) - f’(2)}{3} \ge 4 \Rightarrow f’(5) \ge 17$. Hence $f(5) + f’(5) \ge 28$.
BETA
