Answer
The absolute maximum is $f(3) = 4$.
There is no local maximum. There is no absolute or local minimum.
Work Step by Step
$f(x) = \frac{1}{2}(3x-1)$, $~~x \leq 3$
We can rewrite the equation as follows:
$f(x) = \frac{3}{2}x-\frac{1}{2}$
The slope is $\frac{3}{2}$
The y-intercept is $-\frac{1}{2}$
The absolute maximum is $f(3) = 4$