#### Answer

The seasonal maximum occurs around the end of March each year.
The seasonal minimum occurs around the end of September each year.

#### Work Step by Step

$L(x) = 0.022x^2+0.55x+316+3.5~sin~2\pi x$
The seasonal maximum occurs when $sin~2\pi x = 1$:
$sin~2\pi x = 1$
$2\pi x = \frac{\pi}{2}+2\pi~n$
$x = \frac{1}{4}+n$
$x = \frac{3}{12}+n$
The seasonal maximum occurs at the end of the third month each year. The seasonal maximum occurs around the end of March each year.
The seasonal minimum occurs when $sin~2\pi x = -1$:
$sin~2\pi x = -1$
$2\pi x = \frac{3\pi}{2}+2\pi~n$
$x = \frac{3}{4}+n$
$x = \frac{9}{12}+n$
The seasonal minimum occurs at the end of the ninth month each year. The seasonal minimum occurs around the end of September each year.