Extrema,Increasing/Decreasing

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

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

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

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

Tags

CCSS.HSA.REI.D.10

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Tags

CCSS.HSF.IF.B.4

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSS.ID.C.7

True or false: all critical points are extrema

• True

• False

Tags

CCSS.HSF.IF.C.7

CCSS.HSA.REI.D.10

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,∞)
• (0,1) and (-1,0)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

If given f'(x) how would you find the intervals which the graph f(x) has a positive slope?

• f'(x) < 0 (negative)
• f'(x) > 0 (positive)
• f'(x) is increasing
• Can't be determined

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

Which graph is the derivative of the top graph?

• A
• B
• C
• D