Practicing Success
Practicing Success
CUET Preparation Today
If $f(x)=x e^{x(1-x)}$, then f(x) is |
increasing on $\left[-\frac{1}{2}, 1\right]$ decreasing R increasing on R decreasing on $\left[-\frac{1}{2}, 1\right]$ |
increasing on $\left[-\frac{1}{2}, 1\right]$ |
$f(x)=x e^{(1-x)} \Rightarrow f'(x)=e^{x(1-x)}+x e^{x(1-x)(1-2 x)}$ $\Rightarrow f'(x)=e^{x(1-x)}\left(1+x-2 x^2\right)$ i.e. if $1+x-2 x^2 \geq 0$, i.e. $2 x^2-x-1 \leq 0$ $\Rightarrow(2 x+1)(x-1) \leq 0 \Rightarrow -\frac{1}{2} \leq x \leq 1$. |
