SLIDE 1
Rates of Change
Michael Freeze
MAT 151 UNC Wilmington
Summer 2013
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Section 3.3 :: Rates of Change
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Rates of Change Michael Freeze MAT 151 UNC Wilmington Summer 2013 - - PowerPoint PPT Presentation
Rates of Change Michael Freeze MAT 151 UNC Wilmington Summer 2013 - - PowerPoint PPT Presentation
Rates of Change Michael Freeze MAT 151 UNC Wilmington Summer 2013 1 / 8 Section 3.3 :: Rates of Change 2 / 8 Marginal Revenue The revenue (in thousands of dollars) from producing x units of an item is R ( x ) = 10 x 0 . 002 x 2 . (a)
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SLIDE 3
Marginal Revenue
The revenue (in thousands of dollars) from producing x units of an item is R(x) = 10x − 0.002x2. (a) Find the average rate of change of revenue when production is increased from 1000 to 1001 units.
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SLIDE 4
Marginal Revenue
The revenue (in thousands of dollars) from producing x units of an item is R(x) = 10x − 0.002x2. (b) Find and interpret the instantaneous rate of change of revenue with respect to the number
- f items produced when 1000 units are
- produced. (This number is called the marginal
revenue at x = 1000.)
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SLIDE 5
Marginal Revenue
The revenue (in thousands of dollars) from producing x units of an item is R(x) = 10x − 0.002x2. (c) Find the additional revenue if production is increased from 1000 to 1001 units.
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SLIDE 6
Marginal Revenue
The revenue (in thousands of dollars) from producing x units of an item is R(x) = 10x − 0.002x2. (d) Compare your answers for parts a and c. What do you find? How do these answers compare with your answer to part b?
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SLIDE 7
Flu Epidemic
Epidemiologists in College Station, Texas, estimate that t days after the flu begins to spread in town, the percent of the population infected by the flu is approximated by p(t) = t2 + t for 0 ≤ t ≤ 5. (a) Find the average rate of change of p with respect to t over the interval from 1 to 4 days. (b) Find and interpret the instantaneous rate of change of p with respect to t at t = 3.
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SLIDE 8
Velocity
The distance of a particle from some fixed point is given by s(t) = t2 + 5t + 2, where t is time measured in seconds. Find the average velocity of the particle over the following intervals. (a) 4 to 6 seconds (b) 4 to 5 seconds (c) Find the instantaneous velocity of the particle when t = 4.
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