Find the maximum and the minimum values, if any, without using derivatives of the following functions: f (x) = 4x^2 – 4x + 4 on R

Given $f(x)=4 x^{2}-4 x+4$ on $R$
$=4 x^{2}-4 x+1+3$
By grouping the above equation we get,
$
=(2 x-1)^{2}+3
$
Since, $(2 x-1)^{2} \geq 0$
$
\begin{array}{l}
=(2 x-1)^{2}+3 \geq 3 \\
=f(x) \geq f(1 / 2)
\end{array}
$
Thus, the minimum value of $f(x)$ is 3 at $x=1 / 2$
Since, $f(x)$ can be made large. Therefore maximum value does not exist.