Find the critical points of the function f (x) = 5x^{2} + 4x - 2.

First we take the derivative:

f '(x) = 10x + 4.

Since f '(x) is defined everywhere, we can move right on to finding the roots of f '(x). We need to solve the equation

f '(x) = 0.

Here we go:

This means -2/5 is a critical point - in fact, our only critical point. If we look at the graph, this makes sense, so long as we zoom in enough to see what the graph looks like around x = -2/5: