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LETU MATH 1303 - Concavity and Rates of Change

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Concavity and Rates of ChangeChanging Rate of ChangeSlide 3Slide 4Slide 5Try It OutAssignmentConcavity and Rates of ChangeLesson 2.5Changing Rate of ChangeNote that the rate of change of the curve of the top of the gate is changingConsider how it is changing …Increasing?Decreasing?What effect does that have on the curve?Consider how it is changing …Increasing?Decreasing?What effect does that have on the curve?Concavity and Rates of ChangeWhat do the graphs below have in common?How are they different? Specifically, look at the changing rate of changeBoth are increasing functionsThe slope (rate of change) is increasingThe slope (rate of change) is decreasingConcavity and Rates of ChangeAn increasing positiverate of change is concave UPA decreasing positiverate of change isconcave DOWNSlope is becoming less positiveSlope is becoming more positiveConcavity and Rates of ChangeIncreasing negativerate of change is concave DOWNDecreasing negativerate of change isconcave UPSlope is becoming less negativeSlope is becoming more negativeTry It OutGiven the following tableCalculate the rates of change for successive pairs of points – are the slopes increasing or decreasing?Predict concave up or downNow Plot the pointsConcave up or concave down?x 12 15 18 21H(x) 21.40 21.53 21.75 22.02AssignmentLesson 2.5Page 95Exercises 1 – 19


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