JEE PYQ: Application Of Derivatives Question 77
Question 77 - 2019 (11 Jan Shift 2)
Let $f(x) = \frac{x}{\sqrt{a^2 + x^2}} - \frac{d - x}{\sqrt{b^2 + (d-x)^2}}$, $x \in \mathbb{R}$, where $a, b$ and $d$ are non-zero real constants. Then:
(1) $f$ is an increasing function of $x$
(2) $f$ is a decreasing function of $x$
(3) $f’$ is not a continuous function of $x$
(4) $f$ is neither increasing nor decreasing function of $x$
Show Answer
Answer: (1)
Solution
$f’(x) = \frac{a^2}{(a^2+x^2)^{3/2}} + \frac{b^2}{(b^2+(d-x)^2)^{3/2}} > 0$ for all $x$. So $f$ is increasing.
BETA
