Mean Value Theorem

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.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.HSF.IF.B.6

CCSS.8.F.B.4

What is the average rate of change of the function below over the indicated interval?
f(x) = 12√(x),  [1,16]

• 12 / 5
• 1
• 0
• 36

Tags

CCSS.HSF.IF.B.6

What is the derivative of
f(x) = 12√(x) ?  Read the answer choices carefully - there are subtle differences between some of them.

• 6√(x)
• ⁶ / _√(x)
• 12√(x)
• ¹² / _√(x)

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) = 12√(x),  [1,16]

• 2.5
• 6.25
• 14.4
• 6

Tags

CCSS.HSF.IF.B.6

What is the average rate of change of the function below over the indicated interval?
f(x) = x² + 5x + 5,  [-2,6]

• 9
• 1
• 72
• 0

Tags

CCSS.HSF.IF.B.6

What is the derivative of
f(x) = x² + 5x + 5 ?

• 2x + 5
• x² + 5
• 5x + 5
• 2x - 5

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 +5x +5,  [-2,6]

• 2
• -2
• 7
• -7

Tags

CCSS.HSF.IF.B.6

What is the derivative of
f(x) = ^(x-4)/_(x+1) ?

• f'(x) = ⁵ / _(x+1)²
• f'(x) = ^-3 / _(x+1)²
• f'(x) = ^(2x-3) / _(x+1)²
• f'(x) = ^(2x+5) / _(x+1)²