Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change.

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Extreme Values of Functions

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Presentation transcript:

Lesson 1-4 (Part 2) Using calculators to find extreme values Average Rates of Change

I Do: Find extreme values using a calculator Approximate to the nearest thousandths the relative or absolute extrema of the function. State the x-value(s) where they occur.

Answer: relative minima: (–1.47, 0.80); relative maximum: (–0.20, 4.20); absolute minima: (1.67, –5.51)

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 x 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?

You Do: Approximate to the nearest thousandths the relative or absolute extrema of f (x) = x 3 + 2x 2 – x – 1 State 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)

Key Concept3

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].

Answer Answer:12 The average rate of change on the interval [–3, –1] is 12. The graph of the secant line supports this conclusion.

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].

Answer Answer:–10

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 t 1 and 2 for t 2. Evaluate d(2) and d(1). Simplify.

Class Practice 1.4 Page 41 ( 22 – 28, 34 – 38 even ) Page 44 ( 5, 7, 16, 17, 18 )