Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.
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Transcript of Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.
![Page 1: Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.](https://reader035.fdocuments.us/reader035/viewer/2022070413/5697bf901a28abf838c8e15a/html5/thumbnails/1.jpg)
Lesson 1-4(Part 2)
Using calculators to find extreme values
Average Rates of Change
![Page 2: Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.](https://reader035.fdocuments.us/reader035/viewer/2022070413/5697bf901a28abf838c8e15a/html5/thumbnails/2.jpg)
I Do: Find extreme values using a calculatorApproximate to the nearest thousandths the
relative or absolute extrema of the function. State the x-value(s) where they occur.
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![Page 4: Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.](https://reader035.fdocuments.us/reader035/viewer/2022070413/5697bf901a28abf838c8e15a/html5/thumbnails/4.jpg)
Answer: relative minima: (–1.47, 0.80); relative maximum: (–0.20, 4.20);absolute minima: (1.67, –5.51)
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We Do: Use Extrema for Optimization
FUEL ECONOMY Advertisements for a new car claim that a tank of gas will take a driver and three passengers about 360 miles. After researching on the Internet, you find the function for miles per tank of gas for the car is
f (x) = 0.025x 2 + 3.5x + 240
where x is the speed in miles per hour . What speed optimizes the distance the car can travel on a tank of gas? How far will the car travel at that optimum speed?
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You Do:
Approximate to the nearest thousandths the relative or absolute extrema of
f (x) = x 3 + 2x
2 – x – 1State the x-value(s) where they occur.
A. relative minimum: (0.22 –1.11);relative maximum: (–1.55, 1.63)
B. relative minimum: (–1.55, 1.63); relative maximum: (0.22, –1.11)
C. relative minimum: (0.22, –1.11);relative maximum: none
D. relative minimum: (0.22, 0); relative minimum: (–0.55,0)relative maximum: (–1.55, 1.63)
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Key Concept3
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I Do: Find Average Rates of Change
Find the average rate of change of f (x) = –2x
2 + 4x + 6 on the interval [–3, –1].
![Page 9: Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.](https://reader035.fdocuments.us/reader035/viewer/2022070413/5697bf901a28abf838c8e15a/html5/thumbnails/9.jpg)
Answer
Answer: 12
The average rate of change on the interval [–3, –1] is 12. The graph of the secant line supports this conclusion.
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You Do: Find Average Rates of Change
Find the average rate of change of f (x) = –2x
2 + 4x + 6 on the interval [2, 5].
![Page 11: Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.](https://reader035.fdocuments.us/reader035/viewer/2022070413/5697bf901a28abf838c8e15a/html5/thumbnails/11.jpg)
Answer
Answer: –10
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GRAVITY The formula for the distance traveled by falling objects on the Moon is d (t) = 2.7t
2, where d
(t) is the distance in feet and t is the time in seconds. Find and interpret the average speed of the object for the time interval of 1 to 2 seconds.
Find Average Speed
Substitute 1 for t1 and 2 for t2.
Evaluate d(2) and d(1).
Simplify.
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Class Practice1.4 Page 41 ( 22 – 28, 34 – 38 even )
Page 44 ( 5, 7, 16, 17, 18 )