Deck 29 Estimating Rates of Change

Question 1

When a function reaches a maximum value (at a peak), the rate of change is 0.

Answer 1

True

Question 2

Suppose and .Use this information to estimate the value of when . ​

A) 0
B) 150
C) 3
D) -150

Answer 2

150

Question 3

Use an increment of 0.3 to estimate the value of at if .Round your answer to two decimal places. ​

A) 0.44
B) 1.47
C) 0.00
D) None of the above

Answer 3

1.47

Question 4

The value of can be calculated exactly from a table of values.

Question 5

To get a good estimate of the value of we should use a very short interval to calculate the average rate of change for .

Question 6

If f is the linear function then is: ​

A) 5
B) 8
C)
D) 0

Question 7

A ball is tossed upward and then falls to the ground.Its height after t seconds is given by the function .At the time the rock reaches its peak, what can be said about ? ​

A) is positive.
B) is negative.
C) is zero.
D) None of the above

Question 8

Use an increment of 0.3 to estimate the value of at if .Round your answer to two decimal places. ​

A) -0.13
B) -0.04
C) 0.00
D) None of the above

Question 9

A ball is tossed upward and then falls to the ground.Its height after t seconds is given by the function .During the period the rock is rising, what can be said about ? ​

A) is positive.
B) is negative.
C) is zero.
D) None of the above

Question 10

A balloon is floating upward.Its height in feet t seconds after release is given by the function .We know that and is 4 when t is 3.Use this information to estimate the height of the balloon 9 seconds after release. ​

A) 24 feet
B) 15 feet
C) 35 feet
D) None of the above

Question 11

Suppose and .Use this information to estimate the value of when . ​

A) 0
B) -15
C) 3
D) 15

Question 12

Use an increment of 0.02 to estimate the value of at if . ​

A) 0.0404
B) 2.02
C) 0
D) None of the above

Question 13

Suppose and .Use this information to estimate the value of when . ​

A) 0
B) 50
C) -50
D) -1

Question 14

Use an increment of 0.03 to estimate the value of at if .Round your answer to two decimal places. ​

A) 0.02
B) 0.82
C) 0
D) None of the above

Question 15

If f is the linear function then is: ​

A) 4
B) -3
C) -4
D) 0

Question 16

The value of can be approximated using the average rate of change for .

Question 17

A ball is tossed upward and then falls to the ground.Its height after t seconds is given by the function .During the period the rock is falling, what can be said about ? ​

A) is positive.
B) is negative.
C) is zero.
D) None of the above

Question 18

Suppose and .Use this information to estimate the value of when . ​

A) 0
B) 20
C) -4
D) -20

Question 19

Use an increment of 0.2 to estimate the value of at if . ​

A) 0
B) 4.92
C) 24.6
D) None of the above

Question 20

Water is draining from a pond.The amount of water, in gallons, remaining in the pond t minutes after draining begins is given by the function .We know that and is -579 when t is 9.Use this information to estimate the amount of water in the pond 16 minutes after draining begins. ​

A) 2,309 gallons
B) 1,160 gallons
C) 4,634 gallons
D) None of the above

Question 21

A population changes with time.Its level after t years is given by the function .Over a certain period, the population is declining.What can be said about over this period? ​

A) is positive.
B) is negative.
C) is zero.
D) is linear.

Question 22

A population changes with time.Its level after t years is given by the function .After a period of population increase, the population reaches a maximum value.What can be said about at this time? ​

A) is positive.
B) is negative.
C) is zero.
D) is linear.

Question 23

The profit earned when n items are produced is given by the function .If either increasing production or decreasing production will result in a decrease in profits, what can be said about marginal profit ? ​

A) is positive.
B) is negative.
C) is zero.
D) is linear.

Question 24

The profit earned when n items are produced is given by the function .If increasing production will result in an increase in profits, what can be said about marginal profit ? ​

A) is positive.
B) is negative.
C) is zero.
D) is linear.

Question 25

A population changes with time.Its level after t years is given by the function .After a period of population decrease, the population reaches a minimum value.What can be said about at this time? ​

A) is positive.
B) is negative.
C) is zero.
D) is linear.

Question 26

The profit earned when n items are produced is given by the function .If increasing production will result in a decrease in profits, what can be said about marginal profit ? ​

A) is positive.
B) is negative.
C) is zero.
D) is linear.

Question 27

A population changes with time.Its level after t years is given by the function .Over a certain period, the population is growing.What can be said about over this period? ​

A) is positive.
B) is negative.
C) is zero.
D) is linear.