Question

Prove that the following functions do not have maxima or minima:

$f\left(x\right)=e^x$

Answer 1

$f\left(x\right)=e^x$

$f^{{}^{\prime }}\left(x\right)=e^x$ and this is positive for all values of $x$.
Which means this function will always be increasing function and hence will never have a minimum or maximum.