Question

If the critical point as well as stationary point of the function $f\left(x\right)=\frac{e^x}{x}$ is $x=a$, then value of $a$ is:

Answer 1

$f\left(x\right)=\frac{e^x}{x}$
The above function is not defined at $x=0$.
Differentiating the function and equating it to zero.
$\frac{{(e}^{x}x-e^x)}{x^2}=0$
$\frac{e^x(x-1)}{x^2}=0$
$e^x$ is positive for all $x$.
Therefore $x=1$ is critical point