Rate Of Change

Question 1

How do you determine the average rate of change between two points on a function?

Answer 1

Find the difference in y-values divided by the difference in x-values (f(b) - f(a)) / (b - a)

Question 2

What is the formula for estimating the instantaneous rate of change at a point?

Answer 2

Use the average rate of change over a small interval around the point

Question 3

How do you determine the instantaneous rate of change at a point on a curve?

Answer 3

Find the derivative of the function at that point or use the slope of the tangent line

Question 4

What does the slope of a distance-time graph represent?

Answer 4

It represents the speed or velocity

Question 5

How do you determine if a value is a maximum based on the instantaneous rate of change?

Answer 5

If the instantaneous rate of change changes from positive to negative, it’s a maximum

Question 6

How do you determine if a value is a minimum based on the instantaneous rate of change?

Answer 6

If the instantaneous rate of change changes from negative to positive, it’s a minimum

Question 7

What does the area under a speed-time graph represent?

Answer 7

It represents the distance traveled

Question 8

How can you use rates of change to create a graphical model?

Answer 8

Plot the points of the function and use the slope between intervals to estimate the curve

Question 9

If a distance-time graph is a straight line, what does that indicate?

Answer 9

It indicates constant speed

Question 10

If a speed-time graph is a straight horizontal line, what does that indicate?

Answer 10

It indicates constant speed or velocity

Question 11

How do you solve a word problem involving the rate of change of a population?

Answer 11

Find the difference in population over time and divide by the time interval

Question 12

What is the meaning of a zero slope on a distance-time graph?

Answer 12

The object is stationary

Question 13

How do you interpret a steep slope on a distance-time graph?

Answer 13

A steep slope indicates a high speed or velocity

Question 14

What is the difference between average rate of change and instantaneous rate of change?

Answer 14

Average rate of change is over an interval, while instantaneous rate of change is at a specific point

Question 15

If the instantaneous rate of change is positive, what does it mean about the function?

Answer 15

The function is increasing at that point

Question 16

If the instantaneous rate of change is negative, what does it mean about the function?

Answer 16

The function is decreasing at that point

Question 17

How do you find the slope of the tangent line to a curve at a specific point?

Answer 17

Find the derivative of the function and substitute the x-value of the point

Question 18

What does a negative slope on a speed-time graph indicate?

Answer 18

It indicates deceleration

Question 19

How can you estimate the instantaneous rate of change from a table of values?

Answer 19

Calculate the average rate of change over very small intervals around the point

Question 20

How do you solve a word problem involving the rate of change of a car’s speed?

Answer 20

Find the change in speed over time and divide by the time interval

Question 21

What does it mean if the instantaneous rate of change at a point is zero?

Answer 21

The point could be a local maximum, minimum, or a point of inflection

Question 22

How do you find the average rate of change from a distance-time graph?

Answer 22

Calculate the total distance traveled divided by the total time

Question 23

How do you interpret a curved distance-time graph?

Answer 23

It indicates changing speed or acceleration

Question 24

If a function has a constant rate of change, what type of function is it?

Answer 24

A linear function

Question 25

What is the relationship between velocity and the rate of change in a distance-time graph?

Answer 25

Velocity is the rate of change of distance with respect to time