Chapter 5~ The Structure & Function of Macromolecules 5.1-5.5.
5.1 analysis of function i
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Transcript of 5.1 analysis of function i
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Analysis of Functions: Increase, Decrease, and Concavity
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Increasing and Decreasing Functions
decreasing
decreasingincreasing
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Theorem
Theorem
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How about an Example?Find the intervals on which is increasingand the intervals on which it is decreasing?
2
_ _ _ _ _ _+ + + + + +
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How about another example?Find the intervals on which is concave upand the intervals on which it is concave down.
1 3/2+ + + + + - - - - - - + + + + +
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Inflection points
Points of inflection occur at the points where:•the derivative equals zero•the derivative doesn’t exist•the function changes concavity
Warning !!!
Asymptotes frequently act as inflection points, so make sure you check concavity changes before making conclusion.
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Let’s get all this togetherexample
Considering find the following :
0 2
+ + + + + +_ _ _
1
_ _ _+ + +
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Find the intervals on which f(x) is increasing, decreasing, concave up, concave down and inflection point.