Question

Let $f: R \rightarrow R$ be defined as,
$f(x) = \begin{cases} -55x, & \text{if } x < -5 \\ 2x^3 -3x^2 -120x, & \text{if } 5 \le x \le 4 \\ 2x^3 -3x^2-36x-336& \text{if } x > 4, \end{cases} $
Let $A=\{ x \in R : f$ is increasing $\} .$ Then $A$ is equal to

• A. $(-\infty,-5) \cup(4, \infty)$
• B. $(-5, \infty)$
• C. $(-\infty,-5) \cup(-4, \infty)$
• D. (-5,-4)$\cup(4, \infty)$

Answer 1

Answer: (D)

$f'(x) = \begin{cases} -55; & x < -5 \\ 6(x - 5)(x+4); & -5 < x <4\\ 6(x-3)(x+2); & x > 4 \end{cases} $
$f ( x )$ is increasing in $x \in(-5,-4) \cup(4, \infty)$