Problem 1: Find the average rate of change of the function over the given interval.
f(x) = x2 + 6x, (1, 3)
Problem 2: Find the average rate of change of the function over the given interval.
A(v) = √v + 7, (2, 9)
Problem 3: Find the average rate of change of the function over the given interval. Give a decimal approximation rounded to three decimal places.
P(t) = 4.6 In t + 1.8, (19, 85)
Problem 4: Find the average rate of change of the function over the given interval. Give a decimal approximation rounded to three decimal places.
N(w) = 8e0.2w, (19, 22)
Problem 5: The table shows a city's closing price, in dollars, of one ounce of gold for various days in a certain year.
|
Date
|
Closing Price
|
|
January 11
|
$542.40
|
|
February 8
|
$546.75
|
|
March 15
|
$556.50
|
|
April 19
|
$623.75
|
|
May 17
|
$698.50
|
a. Compute the average rate of change of the closing price from March 15 to May 17.
b. Find the average rate of change from January 11 to February 8.
Problem 6: Let f(x) be the number, in thousands, of vehicles a manufacturers estimates will be sold when x million dollars are spent on advertising. If f(1.7) = 240, and f(2.3) = 345, compute the average rate of change for 1.7 ≤ * ≤ 2.3.
What does your result mean in this context?
Problem 7: The balance in an investment account years t after the account is opened is given by 8500(1.064t). Compute the average rate of change for 3.5 ≤ t ≤ 4.5.
Problem 8: The height in feet of a baseball, t seconds after being thrown straight upward, is given by
h(t) = 44t - 16t2.
a) Find the average speed of the ball for the following intervals.
(i) 0 ≤ t ≤ 1
(ii) 0.5 ≤ t ≤ 1
(iii) 0.9 ≤ t ≤ 1
(iv) 0.99 ≤ t ≤ 1
(b) Estimate the speed of the ball after 1 second.