Practicing Success
The function $f(x)=x^x$ decreases on the interval. |
(0, e) (0, 1) (0, 1/e) None of these |
(0, 1/e) |
$f(x)=x^x$ (Domain is x > 0) $y=x^x,\log y = x\log x$ Diff. wrt x, $\frac{1}{y}\frac{dy}{dx}=x×\frac{1}{x}+\log x⇒\frac{dy}{dx}=x^x(1+\log x)<0$ When 1 + log x < 0 ⇒ log x < -1 $⇒ x < \frac{1}{e}$ As domain of f(x) is x > 0 f(x) decreases when $0<x<\frac{1}{e}\,\,x∈(0,\frac{1}{e})$ |