JEE PYQ: Application Of Derivatives Question 30
Question 30 - 2020 (03 Sep Shift 1)
The function $f(x) = (3x - 7)x^{2/3}$, $x \in \mathbb{R}$, is increasing for all $x$ lying in:
(1) $(-\infty, 0) \cup \left(\frac{14}{15}, \infty\right)$
(2) $(-\infty, 0) \cup \left(\frac{3}{7}, \infty\right)$
(3) $\left(-\infty, \frac{14}{15}\right)$
(4) $\left(-\infty, -\frac{14}{15}\right) \cup (0, \infty)$
Show Answer
Answer: (1)
Solution
$f’(x) = 3x^{2/3} + (3x-7)\frac{2}{3}x^{-1/3} = \frac{15x - 14}{3x^{1/3}}$. $f’(x) > 0$ when $x \in (-\infty, 0) \cup \left(\frac{14}{15}, \infty\right)$.
BETA
