65. Find the average rate of change of f ( x ) = − 2 x 2 + 4 (a) From 0 to 2 (b) From 1 to 3 (c) From 1 to 4 (d) By hand, graph f and illustrate the average rate of change found in parts (a), (b), and (c).
65. Find the average rate of change of f ( x ) = − 2 x 2 + 4 (a) From 0 to 2 (b) From 1 to 3 (c) From 1 to 4 (d) By hand, graph f and illustrate the average rate of change found in parts (a), (b), and (c).
Solution Summary: The author calculates the average rate of change of a function f (x) = 2 x 2 + 4 and graphs it using the available values.
(d) By hand, graph f and illustrate the average rate of change found in parts (a), (b), and (c).
Expert Solution
To determine
To find: The following values using the function ,
a. Average rate of change of a function from 0 to 2.
Answer to Problem 61AYU
a. Average rate of change of a function from 0 to 2 .
Explanation of Solution
Given:
The function .
Calculation:
It is asked to find the average rate of change of the values from 0 to 2, from 1 to 3 and from 1 to 4. Also graph the function using the available values.
a. The average rate of change of from 0 to 2 is,
Expert Solution
To determine
To find: The following values using the function ,
b. Average rate of change of a function from 1 to 3.
Answer to Problem 61AYU
b. Average rate of change of a function from 1 to 3 .
Explanation of Solution
Given:
The function .
Calculation:
It is asked to find the average rate of change of the values from 0 to 2, from 1 to 3 and from 1 to 4. Also graph the function using the available values.
b. The average rate of change of from 1 to 3 is,
Expert Solution
To determine
To find: The following values using the function ,
c. Average rate of change of a function from 1 to 4.
Answer to Problem 61AYU
c. Average rate of change of a function from 1 to 4 .
Explanation of Solution
Given:
The function .
Calculation:
It is asked to find the average rate of change of the values from 0 to 2, from 1 to 3 and from 1 to 4. Also graph the function using the available values.
c. The average rate of change of from 1 to 4 is,
Expert Solution
To determine
To find: The following values using the function ,
d. Draw the graph by hand and illustrate the average rate of change found in the above parts (a), (b) and (c).
Answer to Problem 61AYU
d.
Explanation of Solution
Given:
The function .
Calculation:
It is asked to find the average rate of change of the values from 0 to 2, from 1 to 3 and from 1 to 4. Also graph the function using the available values.
d. Graph:
The function is decreasing for . The fact that that the average rate of change is negative for any and in the interval indicates that the graph is decreasing at a decreasing rate.
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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