JEE PYQ: Application Of Derivatives Question 57
Question 57 - 2019 (08 Apr Shift 1)
Let $f : [0, 2] \to \mathbb{R}$ be a twice differentiable function such that $f’’(x) > 0$, for all $x \in (0, 2)$. If $\phi(x) = f(x) + f(2-x)$, then $\phi$ is:
(1) increasing on $(0, 1)$ and decreasing on $(1, 2)$
(2) decreasing on $(0, 2)$
(3) decreasing on $(0, 1)$ and increasing on $(1, 2)$
(4) increasing on $(0, 2)$
Show Answer
Answer: (3)
Solution
$\phi’(x) = f’(x) - f’(2-x)$. Since $f’’ > 0$, $f’$ is increasing. For $x < 1$: $x < 2-x$, so $f’(x) < f’(2-x)$, $\phi’ < 0$. For $x > 1$: $\phi’ > 0$.
BETA
