JEE PYQ: Application Of Derivatives Question 43
Question 43 - 2020 (06 Sep Shift 2)
For all twice differentiable functions $f : \mathbb{R} \to \mathbb{R}$, with $f(0) = f(1) = f’(0) = 0$:
(1) $f’’(x) \neq 0$ at every point $x \in (0,1)$
(2) $f’’(x) = 0$, for some $x \in (0,1)$
(3) $f’’(0) = 0$
(4) $f’’(x) = 0$, at every point $x \in (0,1)$
Show Answer
Answer: (2)
Solution
By Rolle’s theorem on $[0,1]$: $f’(c) = 0$ for some $c \in (0,1)$. Since $f’(0) = 0$, by Rolle’s theorem on $[0, c]$: $f’’(x) = 0$ for some $x \in (0, 1)$.
BETA
