The function $f(x)=3 x^{4}+16 x^{3}-30 x^{2}+10$ is increasing for

The function $f(x)=3 x^{4}+16 x^{3}-30 x^{2}+10$ is increasing for
  1. every real value of $x$
  2. $x=0, x=1$ only
  3. $x \in(-5,0) \cup(1, \infty)$
  4. $x \in[0,1]$

Solution

$f(x)=3 x^{4}+16 x^{3}-30 x^{2}+10$ $\therefore f^{\prime}(x)=12 x^{3}+48 x^{2}-60 x$ When $f^{\prime}(x)>0$, we write $\quad x\left(12 x^{2}+48 x-60\right)>0$ $12 x\left(x^{2}+4 x-5\right)>0$ $\therefore f^{\prime}(x)>0$, when $x \in(-5,0) \cup(1, \infty)$

Asked in: MHT CET 2020 (20 Oct Shift 2)

Practice more Applications of Derivatives questions on Aicharya