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

Question

Let $f:R \to R$ be defined as

$$f(x) = \left\{ {\matrix{ { - 55x,} & {if\,x < - 5} \cr {2{x^3} - 3{x^2} - 120x,} & {if\, - 5 \le x \le 4} \cr {2{x^3} - 3{x^2} - 36x - 336,} & {if\,x > 4,} \cr } } \right.$

Let A = {x $ \in $$ R : f is increasing}. Then A is equal to :

$( - 5,\infty )$

$( - \infty , - 5) \cup (4,\infty )$

$( - 5, - 4) \cup (4,\infty )$

$( - \infty , - 5) \cup ( - 4,\infty )$

Solution

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