Answer
f(x) is increasing on $(-\infty, 2)$ and decreasing on $(2,+\infty)$
On $(-\infty,+\infty)$ f(x) achieves a maximum value of -4 at x=2
Work Step by Step
$f(x) =-x^{2}+4x-8$
$f'(x)=-2x+4$
$f'(x)=0 \rightarrow -2x+4 =0 \rightarrow x=2$
Thus, f(x) is increasing on $(-\infty, 2)$ and decreasing on $(2,+\infty)$
On $(-\infty,+\infty)$ f(x) achieves a maximum value of -4 at x=2.
