Extrema and Concavity

Use the sign chart for f'(x).
There is(are) ...

• a local maximum at x = -2.
• a local maximum at x = 4.
• local maxima at x = -2 and x = 4.
• no extrema.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Given the following graph of f', the derivative of f. For what x-value does f have a relative minimum?

• x=-1 and x=4
• x=-3
• x=1
• x=3

Tags

CCSS.HSF.IF.B.4

Find the intervals of concavity for

f(x) = x² + 2x + 1.

• concave up: (-∞,∞)

• concave down: (-∞,∞)

• concave up: (2, ∞)

  concave down: (-∞,2)

• concave up: (-∞,2)

  concave down: (2, ∞)

Find the relative minimum values for f(x)=3x⁴-2x³-9x²

• -1

• 0

• 1.5

• -1 and 1.5

Tags

CCSS.HSF.IF.B.4

CCSS.HSA.APR.B.3

CCSS.HSF.IF.C.7

Identify the interval from the derivative graph where the function is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Over what interval(s) is f(x) concave up? (Be careful this is a graph of f'!)

• (-∞, -3) ∪ (1, ∞)

• (-3, 1)

• (-∞,-3) U (1, ∞)

• (-5, 0)U(2, ∞)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Given the velocity function.  Over what interval(s) is the particle moving left?

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

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

Identify the critical points of the following function:
g(x)=2x³-3x²

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

Tags

CCSS.HSA.APR.B.3

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)
• (-∞, -√3) ∪ (0, √3)
• (-1, 1)
• (-√3, 0) ∪ (√3, ∞)

Tags

CCSS.HSA.APR.B.3

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