MCQ
વિધેય $f(x) = {{\log x} \over x}$ એ . . .. અંતરાલમાં વધતું છે.
- A$(1,\,2e)$
- ✓$(0,e)$
- C$(2, 2e)$
- D$(1/e, 2e)$
$f'(x) = \frac{1}{{{x^2}}} - \frac{{\log x}}{{{x^2}}} = \frac{{1 - \log x}}{{{x^2}}}$
For $f(x)$ to be increasing, $f'(x) > 0$
==> $1 - \log x > 0$ ==> $1 > \log x$ ==> $e > x$
$f(x)$ is increasing in the interval $(0,\,e)$.
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