Download 3.1: Increasing and Decreasing Functions

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A function f is increasing on an interval if for
any 2 numbers x1 and x2 in the interval
x1<x2 implies f(x1) < f(x2)
A function f is decreasing on an interval if for
any 2 numbers x1 and x2 in the interval
x1<x2 implies f(x1) > f(x2)
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If f’(x) > 0 for all x in the interval (a, b), then f
is increasing on the interval (a, b).
If f’(x) < 0 for all x in the interval (a, b), then f
is decreasing on the interval (a, b).
If f’(x) = 0 for all x in the interval (a, b), then f
is constant on the interval (a, b).
What is the derivative?
Where is the derivative positive?
Where is the derivative negative?
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If f is defined at c, then c is a critical number
of f if f’(c) = 0 or f’(c) is undefined.
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Find f’(x)
Locate critical numbers
Set up a number line, test x-values in each
interval
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Find the intervals on which f(x) =x3 – 12x is
increasing and decreasing.
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2
3
Find the intervals on which f x   x is
increasing and decreasing.
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Determine the intervals on which the
following functions are
increasing/decreasing.
x3
f x  
 3x
4
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x2
f x  
x 1
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Checkpoint 6 p. 190