JEE PYQ: Application Of Derivatives Question 51
Question 51 - 2020 (08 Jan Shift 2)
Let $S$ be the set of all functions $f : [0, 1] \to \mathbb{R}$, which are continuous on $[0, 1]$ and differentiable on $(0,1)$. Then for every $f$ in $S$, there exists a $c \in (0,1)$, depending on $f$, such that:
(1) $|f(c) - f(1)| < (1-c)|f’(c)|$
(2) $\frac{f(1) - f(c)}{1 - c} = f’(c)$
(3) $|f(c) + f(1)| < (1+c)|f’(c)|$
(4) None of these
Show Answer
Answer: (4)
Solution
For a constant function $f(x)$, options (1) and (3) don’t hold. By LMVT, option (2) is not guaranteed for $f(c)$ at the same $c$. Hence none of these.
BETA
