Question

What are the local extrema of `f(x)= 4^x` if they exist?

Answer 1

If `f(x)=4^x` has a local extremum at c, then either

`f'(c)=0` or `f'(c)` does not exist.

(The ' symbolizes the first derivative)

Hence

`f'(x)=4^x*ln4`

Which is always positive, so `f'(x)>0` hence the function does not

have a local extrema.