Q. The function $f(x) = 2x^{3} - 3x^{2} + 90x + 174$ is increasing in the interval
A) $\frac{1}{2} < x < 1$
B) $\frac{1}{2} < x < 2$
C) $3 < x < \frac{59}{4}$
D) $- \infty < x < \infty$
Explanation
(d)
Given, $f(x) = 2x^{2} - 3x^{2} + 90x + 174$
$\therefore f^{'}(x)6x^{2} - 6x + 90$
Now, $D = b^{2} - 4ac = 36 - 4 \times 6 \times 90 < 0$
$\therefore f^{'}(x) > 0\forall x \in ( - \infty,\infty)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.