CUET Preparation Today
The function $f(x)=x^x$ decreases on the interval |
$(0, e)$ $(0,1)$ $(0,1 / e)$ none of these |
$(0,1 / e)$ |
Clearly, f(x) is defined for all x > 0. Now, $f(x)=x^x \Rightarrow f'(x)=x^x(1+\log x)$ For f(x) to be decreasing, we must have f'(x) < 0 $\Rightarrow x^x(1+\log x)<0$ $\Rightarrow 1+\log x<0$ $\Rightarrow \log x<-1 \Rightarrow x<e^{-1}$ So, f(x) is decreasing on (0, 1/e). |
