Concavity and Rates of ChangeChanging Rate of ChangeSlide 3Slide 4Slide 5Try It OutAssignmentConcavity and Rates of ChangeLesson 2.5Changing Rate of ChangeNote 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 ChangeWhat 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 ChangeAn increasing positiverate of change is concave UPA decreasing positiverate of change isconcave DOWNSlope is becoming less positiveSlope is becoming more positiveConcavity and Rates of ChangeIncreasing negativerate of change is concave DOWNDecreasing negativerate of change isconcave UPSlope is becoming less negativeSlope is becoming more negativeTry It OutGiven the following tableCalculate the rates of change for successive pairs of points – are the slopes increasing or decreasing?Predict concave up or downNow Plot the pointsConcave up or concave down?x 12 15 18 21H(x) 21.40 21.53 21.75 22.02AssignmentLesson 2.5Page 95Exercises 1 – 19
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