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In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
Our function $f(x) = 3x^4-4x^3-12x^2+3$ is differentiable everywhere on $[-2,3]$, with $f'(x) = 0$ for $x=-1,0,2$. These are the three critical points of $f$ on $[-2,3]$. By the First Derivative Test, $f$ has a relative maximum at $x=0$ and relative minima at $x=-1$ and $x=2$.