Wetzel

Math 140

3.3 – Increasing and Decreasing Functions & The First Derivative Test

Review –

            Given the function, 

            a.)  Find the Critical Numbers.

            b.)  Find any extrema.

            c.)  Find any extrema on the interval [-3, 4].

Now –

            d.)  Determine where f(x) is increasing and/or decreasing.

Def. of Increasing and Decreasing–

            A function  is increasing on an interval if for any two numbers a and b in the interval, a < b implies

            A function  is decreasing on an interval if for any two numbers a and b in the interval, a < b implies

Test for Increasing and Decreasing –

            Let  be a function that is continuous on the closed interval  and differentiable on the open interval .

1. If  for all x in , then  is increasing on .

2. If  for all x in , then  is decreasing on .

3. If  for all x in , then  is constant on .

First-Derivative Sign Diagrams

Ex.:  Construct a First Derivative Sign Diagram for each of the following.

1.)                                                     2.) 

3.)                                                          4.)  ,

HW:  p.186 #9-15odd, 17-27odd (on part c, construct a 1^st derivative sign diagram)