Question

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

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

Answer 1

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

$f^{\prime }\left(x\right)=e^x$

Now, if $f^{\prime }\left(x\right)=0⟹e^x=0$

But, the exponential function can never assume zero for any value of x.

Therefore, there does not exist $c\in R$ such that $f^{\prime }\left(c\right)=0$.

Hence, function f does not have maxima or minima.