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lecture17hout

# lecture17hout - MATH 006 Calculus and Linear...

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MATH 006 Calculus and Linear Algebra (Lecture 17) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 15

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Outline 1 Average Rate of Change 2 Instantaneous Rate of Change 3 Slope of a Tangent 4 The Derivative Albert Ku (HKUST) MATH 006 2 / 15
Average Rate of Change Average Rate of Change Let y = f ( x ). Roughly speaking, the “rate of change” of y is Change in y Change in x More rigorously, we have the following deﬁnition: Deﬁnition For y = f ( x ), the average rate of change from x = a to x = b is f ( b ) - f ( a ) b - a Albert Ku (HKUST) MATH 006 3 / 15

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Average Rate of Change Example The revenue from the sale of x plastic boxes is given by R ( x ) = 20 x - 0 . 02 x 2 , 0 x 1 , 000 . (a) What is the change in revenue if production is changed from 100 boxes to 400 boxes? (b) What is the average rate of change in revenue for this change? Solution (a) The change in revenue is R (400) - R (100) = 4800 - 1800 = 3000. (b) The average rate of change in revenue is 3000 400 - 100 = \$10 per box. Albert Ku (HKUST) MATH 006 4 / 15
Average Rate of Change Example A small ball dropped from a tower will fall a distance of y feet in x seconds, as given by the formula y = 16 x 2 . (a)

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lecture17hout - MATH 006 Calculus and Linear...

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