Difficult# Count Critical Points Given the Derivative

APCALC-IBVNKG

Consider the function $h(x)$ whose derivative is given by,

$$h'(x) = \frac{{{{\cos }^2}(x)}}{{2x}} - \frac{1}{{12}}$$

How many critical points does $h(x)$ have on the open interval $(0, 10)$?