JEE Main 2022 · 28 Jul · Shift 2 · Mathematics Q66

MathematicsSingle correct+4 / -1Question 66 of 90

The function $f(x)=xe^{x(1-x)}$ , $x\in\mathbf R$ , is :

increasing in

\left(-\dfrac12,1\right)

decreasing in

\left(\dfrac12,2\right)

increasing in

\left(-1,-\dfrac12\right)

decreasing in

\left(-\dfrac12,\dfrac12\right)

Answer and worked solution

Official answer: A

Derivative $f'=e^{x-x^2}(1+2x)(1-x)$ , positive on $\left(-\frac12,1\right)$ .

(A)

Topics:Monotonicity

JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 66