Question:
Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as
$f(x)= \begin{cases}-55 x, & \text { if } x<-5 \\ 2 x^{3}-3 x^{2}-120 x, & \text { if }-5 \leq x \leq 4 \\ 2 x^{3}-3 x^{2}-36 x-336, & \text { if } x>4\end{cases}$
Let $A=\{x \in R: f$ is increasing $\} .$ Then A is equal to :
Correct Option: 1,
Solution:
$f(x)=\left\{\begin{array}{ccc}-55 & ; & x<-5 \\ 6\left(x^{2}-x-20\right) & ; & -5
$f(x)=\left\{\begin{array}{lcc}6(x-5)(x+4) & ; & -5
Hence, $f(x)$ is monotonically increasing in interval $(-5,-4) \cup(4, \infty)$