Let f : R $\to$ R be defined as$$f(x) = \left\{ {\matrix{ { - {4 \over 3}{x^3} + 2{x^2} + 3x,} & {x > 0} \cr {3x{e^x},} & {x \le 0} \cr } } \right.$$. Then f is increasing function in the interval

Question

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

$$f(x) = \left\{ {\matrix{ { - {4 \over 3}{x^3} + 2{x^2} + 3x,} & {x > 0} \cr {3x{e^x},} & {x \le 0} \cr } } \right.$$. Then f is increasing function in the interval

$\left( { - {1 \over 2},2} \right)$

(0,2)

$\left( { - 1,{3 \over 2}} \right)$

($-$3, $-$1)

Solution

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