Mean Value and Rolle's Theoren

What is the average rate of change of the function below over the indicated interval?
f(x) = x² - 3x - 28,  [-4,7]

• 0
• 11
• 6
• 66

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

What is the derivative of
f(x) = x² - 3x - 28 ?

• 2x - 3
• 2x + 3
• x - 3
• 2x² - 3x - 28

Tags

CCSS.HSF.IF.A.2

What is x-value at which the function below has the same slope as the average rate of change over the indicated interval?
f(x) = x² - 3x - 28,  [-4,7]

• 1.5
• -1.5
• 0.5
• -0.5

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The value of c guaranteed to exist by the MVT for  $f\left(x\right)=x^2$  on the interval [0,3] is:

• 1

• 2

• 3/2

• 1/2

 $f\left(x\right)=\left(x-3\right)\left(x+1\right)^2,\ \ \ \ \left[-1,3\right]$  

Find the value of c which is guaranteed by Rolle's Theorem.

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

Tags

CCSS.HSA.APR.B.3