Toughest Calculus ever in JEE.

$f(x)$ is a differentiable function and $g(x)$ is a double differentiable function such that $| f(x) | \le 1$ and $f'(x) = g (x)$ .

Let $\large\ { \left( f( 0) \right) }^{ 2 } + { \left( g( 0 ) \right) }^{ 2 } = 9$ .

Then find AT LEAST how many $c \in (-3, 3)$ exists satisfying

$\large\ g (c) \cdot g''(c) < 0$ .