Unformatted text preview: interval to determine
where f is positive and where f is negative.
Example
Determine where f is positive and where f is negative.
1 2
3 Graph f (x ) = x 3 − 2x 2 − 4x + 8 and use the graph to
determine the intervals on which f (x ) is positive and the
intervals on which f (x ) is negative.
f (x ) = x 3 − x .
x
g (x ) =
.
x −1 Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Increasing/Decreasing/Constant Deﬁnition
Suppose f is a function from D into R. Suppose I is an interval in
D.
1 f is increasing on I if x1 , x2 ∈ I with x1 < x2 imply
f (x1 ) < f (x2 ). 2 f is decreasing on I if x1 , x2 ∈ I with x1 < x2 imply
f (x1 ) > f (x2 ). 3 f is constant on I if x1 , x2 ∈ I implies f (x1 ) = f (x2 ). Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Examples.
Example
1 Determine the intervals on which the function f graphed
below is increasing/decreasing. 2 Discuss the end behavior of the function f graphed below.
f (x )
4
y = f (x ) 3
2
1
3 2 1 1 2 3 4 x Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Maximum/ Minimum Values
Deﬁnition
Suppose f is a function from D into R.
1 A global maximum for f on...
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This note was uploaded on 02/10/2014 for the course MATH 1050 taught by Professor K.jplatt during the Spring '14 term at Snow College.
 Spring '14
 K.JPlatt
 Math, Algebra

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