Chapter 4Applications of Derivatives

Extreme Values of Functions

The Rolles TheoremThe mean value theorem

Monotonic Functions and the first derivative testExample:

Find the critical points of and identify the intervals on which f is increasing and decreasing.Solution:

Example:

Find the critical points of and identify the intervals on which f is increasing and decreasing. Find the functions local and absolute extreme values.Solution:

First derivative test for local extrema:

x=0 : f(x) does not change sign

x=1 :f(x) changes from ve to +ve

Local min: f(1)=-3Absolute min: f(1)=-3No local extremumlocal minimum

Tutorial 4Exercises 3.7: 11,25,34,45Exercises 3.8: 20,28,32,41Exercises 4.1: 23,43,48,51,64Exercises 4.2: 4,11Exercises 4.3: 4,18,28,38,47Ref: Thomas Calculus, 12th Edition