Find the points of local maxima or local minima, if any, of the following functions, using the first derivative test. Also, find the local maximum or local minimum values, as the case may be: f (x) = (x – 5)^4

Given $f(x)=(x-5)^{4}$
Differentiate with respect to $x$
$
f(x)=4(x-5)^{2}
$
For local maxima and minima
$
\begin{array}{l}
f(x)=0 \\
=4(x-5)^{2}=0 \\
=x-5=0 \\
x=5
\end{array}
$
$f(x)$ changes from negative to positive as passes through $5 .$
So, $x=5$ is the point of local minima
Thus, local minima value is $f(5)=0$