#### Answer

$x=\frac{1}{3}$

#### Work Step by Step

Find the critical numbers of $f(x) = 4+ \frac{1}{3}x - \frac{1}{2}x^2$
Differentiate and set the derivative $= 0$ to find the critical numbers.
$f'(x) = \frac{1}{3} - x$
$0=\frac{1}{3} - x$
$x=\frac{1}{3}$