Objectives Upon completion of this lesson you should be able to find where functions are increasing or decreasing A function f is increasing on a b if f x 1 lt ID: 257888
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Slide1
Increasing and Decreasing FunctionsSlide2
ObjectivesUpon completion of this lesson, you should be able to:find where functions are increasing or decreasingSlide3
A function f is
increasing on (
a
,
b
) if f (x1) < f (x2) whenever x1 < x2.
A function f is decreasing on (a, b) if f (x1) > f (x2) whenever x1 < x2.
Increasing
Increasing
Decreasing
Increasing/Decreasing FunctionsSlide4
Increasing/Decreasing/ConstantFunctionsSlide5
Example
In the given graph of the function f
(
x
), determine the interval(s) where the function is increasing, decreasing, or constant.
The function is decreasing on the interval (-4, -2)The function is increasing on the interval (-2, 0)The function is decreasing on the interval (0, 2)Slide6
Determine the intervals where
0 4
f
is increasing
onis increasing and where it is decreasing.f is decreasingon
Example
At x = -2 (
ie
. less than 0)
Ie. positive
At x = 1 (ie. btwn
0 and 4)
Ie. negativeAt x = 5 (ie. greater than 4)
Ie
. positive
+ - +