Free Printable Average and Instantaneous Rates of Change

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Average and Instantaneous Rates of Change

Total questions: 11

Worksheet time: 1hrs 6mins

Name

Class

Date

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

1/2

-2

-1/2

What was the average rate of change in the population from 1900 to 1990?

175 million people/year

1.94 million people/year

2.13 million people/year

-1 million people/year

Approximate the instantaneous rate of change of the function at x = -1.

f\left(x\right)=3x^2+2x-1

-4

-1/4

-2

Find the instantaneous rate of change for f(x) at x = 2 for $f\left(x\right)\ =-\frac{3}{4}x^4+2$

-24

- $\frac{3}{2}$

- $\frac{3}{4}$

Find the instantaneous rate of change

88.25

39.5

87.75

88.5

If the position of a particle is represented by s(t) = t² + 2, what is its instantaneous velocity at t = 3?

5 ft/sec

6 ft/sec

3 ft/sec

4 ft/sec

f(x) = 3x² + 12x + 16

Estimate the instantaneous rate of change at x = -1.

About 6

About -6

About 0

About 5

Speed

when a distance l is traveled during a time interval Δt is

the time derivative of the displacement (a limit as the time interval approaches Zero)

is the absolute value of the velocity vector. For a moving object, speed is always positive.

finding the rate of change of a function with respect to one of its variables

Which of the following are ways to find the rate of change?

change in y over change in x

rise over run

subtract y coordinates over subtract x coordinates

all of the above

10.

Which of the following are ways to find the rate of change?

change in y over change in x

rise over run

subtract y coordinates over subtract x coordinates

all of the above

11.

Find the average rate of change of f(x)=2x²+3x-1 from 1 to 2.

-9

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Average and Instantaneous Rates of Change

Total questions: 11

Worksheet time: 1hrs 6mins

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