Post on 23-Feb-2016
description
Section 4.3Increasing and Decreasing Functions and
the First Derivative Test
Relative Maximum f(x)
Relative Extrema
Relative Minimum
f(x)
Relative Extrema
f(x)
Relative Extrema
f(x)
Relative Extrema
Increasing and Decreasing
𝑓 ’ (𝑥 )<0• is
decreasing
𝑓 ’ (𝑥 )=0• is
constant
𝑓 ’ (𝑥 )>0• is
increasing
Use the graph to find the (a) largest open interval where the function is decreasing and the (b) largest open interval where its increasing.
Example 1
Use the graph to estimate where the fnc. is increasing or decreasing. Then find the open intervals analytically.
Example 2
𝒇 (𝒙 )=𝒙𝟒−𝟐 𝒙𝟐
Identify the intervals where the function is increasing or decreasing.
Example 3
𝑓 (𝑥 )=27 𝑥−𝑥3
Identify the intervals where the function is increasing or decreasing.
Example 4
𝑓 (𝑥 )=𝑥+4𝑥
Identify the intervals where the function is increasing or decreasing and locate all relative extrema.
Example 5
𝑓 (𝑥 )=𝑥4−32𝑥+4
Identify the intervals where the function is increasing or decreasing and locate all relative extrema.
Example 6
𝑓 (𝑥 )=𝑥+4𝑥2
Identify the intervals where the function is increasing or decreasing and locate all relative extrema.
Example 7
𝑓 (𝑥 )=(𝑥−1)𝑒𝑥
Identify the intervals where the function is increasing or decreasing and locate all relative extrema.
Example 8
𝑓 (𝑥 )=𝑥+2sin 𝑥 ,0<𝑥<2𝜋
The graph of is given. Sketch the graph of .Example 9
The graph of is given. Sketch the graph of .Example 10
Be sure to be practicing the given problem sets!
Questions?