Let $f: R \rightarrow R$ be defined as $$ f(x)=\left\{\begin{aligned} -\frac{4}{3} x^3+2 x^2+3 x, & x0 \ 3 x e^x, & x \leq 0 \end{aligned}\right. $$ Then $f$ is increasing function in the interval. [JEE Main 2021, 22 Jul (Shift 2)]

Question

Let $f: R \rightarrow R$ be defined as $$ f(x)=\left\{\begin{aligned} -\frac{4}{3} x^3+2 x^2+3 x, & x>0 \ 3 x e^x, & x \leq 0 \end{aligned}\right. $$ Then $f$ is increasing function in the interval. [JEE Main 2021, 22 Jul (Shift 2)]

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Let \(f: R \rightarrow R\) be defined as \[ f(x)=\left\{\begin{aligned} -\frac{4}{3} x^3+2 x^2+3 x, & x>0 \\ 3 x …

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Let \(f: R \rightarrow R\) be defined as \[ f(x)=\left\{\begin{aligned} -\frac{4}{3} x^3+2 x^2+3 x, &amp; x&gt;0 \\ 3 x …

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Let \(f: R \rightarrow R\) be defined as \[ f(x)=\left\{\begin{aligned} -\frac{4}{3} x^3+2 x^2+3 x, & x>0 \\ 3 x …