Mathematics · 2021
JEE Main · 22 July 2021, Shift 2 · Q75
Let f: R → R be defined as f(x)= {-4/3 x^3+2 x^2+3 x, x>0; 3 x e^x, x ≤ 0} Then f is increasing function in the interval.
Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as
$$f(x)= \begin{cases}-\frac{4}{3} x^3+2 x^2+3 x, & x>0 \\ 3 x \mathrm{e}^x, & x \leq 0\end{cases}
$$
Then $\displaystyle f$ is increasing function in the interval.
Official answer
(3)
$\displaystyle \left(-1, \frac{3}{2}\right)$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.