QPaperGen

We have \( f(x) = (x - 1)^2 + 3 \)

\[
f'(x) = 2(x - 1) \Rightarrow f'(x) = 0 \Rightarrow x = 1
\]

Now evaluate \( f \) at endpoints and critical point:
\[
f(-3) = (-3 - 1)^2 + 3 = 16 + 3 = 19 \\
f(1) = (1 - 1)^2 + 3 = 0 + 3 = 3
\]

\(\textbf{Absolute maximum}\) is \( 19 \) at \( x = -3 \) and \(\textbf{Absolute minimum}\) is \( 3 \) at \( x = 1 \)