Application of Derivatives

Critical PointsDefinition

We say that  is a critical point of the function f(x) if    exists and if either of the following are true.                           

Example 1 Determine all the critical points for the function.

Solution: We first need the derivative of the function in order to find the critical points.

Now, our derivative is a polynomial and so will exist everywhere. Therefore the only critical points will be those values of x which make the derivative zero.

Because this is the factored form of the derivative it’s easy to identify the three critical points. They are,

ANS: