AP Calculus Applications of the Derivative Review

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points

Tags

CCSS.HSA.APR.B.3

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)
• (0,1)
• (-∞,-1) and (1,∞)
• (-1,0) and (1,∞)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

f' is given, which could be f?

• A
• B
• C

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing

Over what interval(s) is f(x) decreasing?

• (-3, 1)
• (-∞, -5) ∪ (0, 2)
• (-∞, -3) ∪ (1, ∞)
• (-5, 0) ∪ (2, ∞)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Over what interval(s) is the particle moving left?

• (0, 8)
• (0, 7) ∪ (10, 12)
• (0, 6) ∪ (10, 12)
• (3, 8)

Tags

CCSS.HSF-IF.C.7B

When is the particle at rest?

• t = 3 and t = 8
• (3, 8)
• (6, 7)
• t = 6 and t = 7 and t = 10

Tags

CCSS.HSF.IF.B.4

Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

What will be true at an inflection point?  (select the best answer)

• f(x)=0
• f'(x)=0
• f''(x)=0
• The function is undefined