Calculus Area Volume and Theorems

• A

• B

• C

• D

• A
• B
• C
• D

Tags

CCSS.HSA.REI.C.7

• A

• B

• C

• A
• B
• C
• D

Disk/Washer Method

• B

• C

• D

• E

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 function h is continuous on the closed interval [-2, 5] and differentiable on the open interval (-2, 5) . If f (-2) = 3 and f (5) =-11, which of the following statements could be false?

• There exists a c on the interval (-2, 5) such that f'(c) = 0. 
• There is an absolute maximum value on the interval [-2, 5]
• There exists a con on the interval (-2, 5) such that f(c) = 0. 
• There exists a c on the interval (-2, 5) such that f'(c) = -2. 

Let g be a function that is differentiable over the interval (2, 9) . Giveng(3) = 5 , g(6) = -2 , and g(8) = 5 , which of the following must be true?
I. g has at least one horizontal tangent line.
II. g has at least 2 zeros.
III. For some c in the interval (3, 6), f'(c) = -7/3. 

• II only
• II and III
• I and II
• I, II, and III

If f(x) = x³ + 1 then there exists a number c in the interval (0, 1) that satisfies the conclusion of the Mean Value Theorem. Which of the following could be c ?

• -√(1/3)
• √(1/3)
• 1
• 2

The function g is continuous on the interval [0, 5] and has select values in the table. The equation g(x) = 1 must have at least 2 solutions in the interval [0, 5] if k = 

• 6
• 2
• 0
• 1

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11