Differential Equations

The function $f$ has a local minimum at $x = \frac{1}{\sqrt{3}}$

The function $f$ has a local maximum at $x = \frac{1}{\sqrt{3}}$

The function $f$ is increasing in the interval $(1, 2)$

If $g(x) = 4x^3 - 5x^2 + \frac{3}{2}x$ for $x > 0$, then the number of elements in the set \(\{x \in (0, \infty) : f(x) = g(x) \}\)
is $2$