Extrema and Concavity

When f'(x) changes from negative to positive, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

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

When f'(x) changes from positive to negative, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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, ∞)

 If (a,b) is a local minimum, then what will be true about f'(a)?

• It's positive
• It's negative
• It's zero
• Cannot be determined

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.HSF.IF.C.7

CCSS.HSA.APR.B.3

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

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

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