Average and Instantaneous Rates of Change

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

• 2
• 1/2
• -2
• -1/2

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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

 $f\left(x\right)=3x^2+2x-1$  

• -4

• -1/4

• 3

• -2

Tags

CCSS.HSF.IF.B.6

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

• -24

• - $\frac{3}{2}$  

• 24

• - $\frac{3}{4}$  

Find the instantaneous rate of change

• 88.25

• 39.5

• 87.75

• 88.5

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

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

Tags

CCSS.HSF.IF.B.6

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

Tags

CCSS.HSF-LE.A.1B

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

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6