JEE PYQ: Application Of Derivatives Question 64
Question 64 - 2019 (10 Apr Shift 1)
Let $f(x) = e^x - x$ and $g(x) = x^2 - x$, $\forall x \in \mathbb{R}$. Then the set of all $x \in \mathbb{R}$, where the function $h(x) = (f \circ g)(x)$ is increasing, is:
(1) $\left[-1, -\frac{1}{2}\right] \cup \left[\frac{1}{2}, \infty\right)$
(2) $\left[0, \frac{1}{2}\right] \cup [1, \infty)$
(3) $[0, \infty)$
(4) $\left[-\frac{1}{2}, 0\right] \cup [1, \infty)$
Show Answer
Answer: (2)
Solution
$h’(x) = (2x-1)e^{x^2-x} - 1 $… For $h’(x) \ge 0$: $(2x-1)(e^{x^2-x} - 1) \ge 0$. Both factors have same sign when $x \ge 1$ or $0 \le x \le \frac{1}{2}$.
BETA
