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

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Answer 1 · 2015-11-16T03:57:16

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.

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