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Section 2.4 Interpretations of the Derivative

Section 2.4 Interpretations of the Derivative. Alternative Notation for Derivative. The d stands for ‘small difference in’ Notice it is similar to our rate of change notation Note:.

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Section 2.4 Interpretations of the Derivative

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  1. Section 2.4Interpretations of the Derivative

  2. Alternative Notation for Derivative • The d stands for ‘small difference in’ • Notice it is similar to our rate of change notation • Note:

  3. The revenue, R (in thousands of dollars) for a certain item is related to the number of items sold, x (given in hundreds of items) by R = f(x). Interpret the following statements: • f(1.4) = 10 • f’(1.4) = 0.7 • f’(20) = -1

  4. Let f(t) be the number of inches of rain that has fallen since midnight, where t is the time in hours. Interpret the following in practical terms, giving units. • f(10) = 1.4 • f’(10) = 0.1 • f’’(10) = -0.2 • f -1(1) = 2 • (f-1(1.4))’ = 3 • Approximately what is f(11) and what does it mean in this context?

  5. f(10) = 1.4 At 10am, 1.4 inches of rain have fallen • f’(10) = 0.1 At 10am, the amount of rainfall is increasing by 0.1 inches per hour • f’’(10) = -0.2 At 10 am, the amount that the rainfall is accumulating is decreasing • f -1(1) = 2 The rainfall reached 1 inch at 2am • (f-1(1.4))’ = 3 When the rainfall was 1.4 inches, it was taking 3 hours to accumulate an inch

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