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5.2 - MATH1081 Monday,February28 Chapter5Section2...

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MATH 1081 Monday, February 28 Chapter 5 – Section 2 RELATIVE EXTREMA Homework #7 (due 3/7) Section 5.2 #30, 36, 46, 56 Section 5.3 #30, 44, 52, 78, 82, 94 Clicker Check-in: Choose any letter to check in now.
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Last time, we used the sign of the first derivative of a function to determine on which intervals the function was increasing and on which intervals the function was decreasing. To summarize, on intervals where f ' x ( ) > 0 the function f x ( ) is increasing (the graph goes upward from left to right) and on intervals where f ' x ( ) < 0 the function f x ( ) is decreasing (the graph goes downward from left to right). We continue that discussion today. So really, there is nothing new in the way of techniques covered in this section. There are just some new vocabulary and formalization of some ideas.
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Now, suppose that we have the following results from the analysis of the sign of f ' x ( ) . What can we say about the value f 3 ( ) ? What can we say about the value f 1 ( ) ?
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For example, consider the graph of the function f x ( ) here.
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As usual, determining relative extrema by looking at a graph of
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