Question

Function $f\left(x\right)=e^{-1/x}(x>0)$ is-

• A. Increasing
• B. Decreasing
• C. Not monotonic
• D. None of these

Answer 1

The correct option is A Increasing

$f\left(x\right)=e^{-\frac{1}{x}}$

$f^{\prime }\left(x\right)=e^{-\frac{1}{x}}\times \frac{d}{dx}\left(-\frac{1}{x}\right)$

$=e^{-\frac{1}{x}}\times \left(-1\right)\times \frac{-1}{x^2}$

$=\frac{1}{x^2}\times e^{-\frac{1}{x}}>0\forall x$

so, $f\left(x\right)$ is increasing