Lesson 1-4(Part 2)

Using calculators to find extreme values

Average Rates of Change

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.

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 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?

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)

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 t1 and 2 for t2.

Evaluate d(2) and d(1).

Simplify.

Class Practice1.4 Page 41 ( 22 – 28, 34 – 38 even )

Page 44 ( 5, 7, 16, 17, 18 )