JEE PYQ: Application Of Derivatives Question 4
Question 4 - 2021 (16 Mar Shift 2)
Let $f$ be a real valued function, defined on $\mathbb{R} - {-1, 1}$ and given by
$$f(x) = 3\log_e\left|\frac{x-1}{x+1}\right| - \frac{2}{x-1}$$
Then in which of the following intervals, function $f(x)$ is increasing?
(1) $(-\infty, -1) \cup \left(\left[\frac{1}{2}, \infty\right) - {1}\right)$
(2) $(-\infty, \infty) - {-1, 1}$
(3) $\left(-1, \frac{1}{2}\right]$
(4) $\left(-\infty, \frac{1}{2}\right] - {-1}$
Show Answer
Answer: (1)
Solution
$f’(x) = \frac{3}{x-1} - \frac{3}{x+1} + \frac{2}{(x-1)^2} = \frac{4(2x-1)}{(x-1)^2(x+1)}$. $f’(x) \ge 0$ when $x \in (-\infty, -1) \cup [\frac{1}{2}, 1) \cup (1, \infty)$.
BETA
