AP Calculus Unit 3 Review

The Mean Value Theorem applies to f(x) = 3x - x² on the interval [2, 5]. Find the value of x satisfying mean value theorem.

• 2

• -4

• 3.5

• -2

Find the value of x that satisfies the mean value theorem over the indicated interval?

f(x) = x² +5x +5,  [-2,6]

• 2
• -2
• 5

• 3.5

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

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.8.F.B.4

CCSS.HSF.IF.B.6

Find dy/dx by Implicit Differentiation 
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx at a given point.

• 5/4
• 4/5
• 1
• -5

Tags

CCSS.HSF-BF.B.4A

Find dy/dx
xy+y²=2

• -y/(x+2y)
• y/(x+2y)
• -3y/x
• -3x/y