Write out the original equation. We'll use "f(x) = x^2 - 4" for this example.
Set the equation to zero and solve, so:
"0 = x^2 - 4 -> 4 = x^2 -> x = 2, -2"
Your first critical points, the zeros, are at (2, 0), (-2, 0).
Find the derivative of your original equation.
"dy/dx = 2x"
Set the derivative equal to zero and solve.
"0 = 2x -> x = 0"
Substitute your answer into the original equation.
"f(x) = x^2 - 4 -> f(x) = -4"
Your third critical point is (0, -4). Coincidentally, this is a local minimum.