QPaperGen

\[
f'(x) = 3x^2 - 12x + 9 = 3(x - 1)(x - 3)
\Rightarrow f'(x) = 0 \Rightarrow x = 1, 3
\]
\[
f''(x) = 6x - 12
\Rightarrow f''(1) = -6 < 0 \Rightarrow \text{Local maximum}
\Rightarrow f(1) = 1 - 6 + 9 + 15 = 19
\]
\[
f''(3) = 6 > 0 \Rightarrow \text{Local minimum}
\Rightarrow f(3) = 27 - 54 + 27 + 15 = 15
\]