*x, f(x)*) is called a

**critical point**of

*f(x)*if

*x*is in the domain of the function and either

*f′(x)*= 0 or

*f′(x)*does not exist. The geometric interpretation of what is taking place at a critical point is that the tangent line is either horizontal, vertical, or does not exist at that point on the curve.

**Example 1:** Find all critical points of

Because *f(x)* is a polynomial function, its domain is all real numbers.

hence, the critical points of *f(x)* are (−2,−16), (0,0), and (2,−16).

**Example 2:** Find all critical points of *f(x)*= sin *x* + cos *x* on [0,2π].

The domain of *f(x)* is restricted to the closed interval [0,2π].

hence, the critical points of *f(x)* are