1.1 Class Notes - 3.3. Rates of Change Average rate of...

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3.3. Rates of Change Average rate of change between s and t If f is the position this is the average speed If f(1)=50 and f(3)=174 miles then ARC = 124/2 = 62 miles per hour () ( ) ft fs ARC ts = f(x) = 10 + 18x + 9x 2 –2x 3 -150 -100 -50 0 50 100 150 200 250 - 4- 3 - 2- 101234567 f(1)=35, f(0)=10, ARC = 25 10 15 20 25 30 35 0 0.2 0.4 0.6 0.8 1 ARC = (1.888)/(0.1)= 18.88 11.888 10 10.5 11 11.5 12 0 0.02 0.04 0.06 0.08 0.1 ARC = (.1809)/(.01) = 18.09 10.1809 10 10.04 10.08 10.12 10.16 10.2 0 0.002 0.004 0.006 0.008 0.01 ARC = (.018009)/(.001) = 18.009 10.018009 10 10.004 10.008 10.012 10.016 10.02 0 0.0002 0.0004 0.0006 0.0008 0.001
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h ave rate of change 12 5 0.1 18.88 0.01 18.09 0.001 18.0009 limit 18 0 () ( ) '( ) lim h fx h fx fx h +− = Derivative of f Is the Instantaneous rate of change If f(x) = number on the odometer f (x) = number on the speedometer 0 ( ) lim h h = Why is the derivative = 18?
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1.1 Class Notes - 3.3. Rates of Change Average rate of...

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