Unit 4 AP Calculus Review

• Increasing and concave upward

• decreasing and concave upward

• increasing concave downward

• decreasing concave downward

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

• Relative maximum

• Relative minimum

• point of inflection

• cannot be determined

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• A relative maximum at x=a

• A relative minimum at x=a

• No relative extrema at x=a

• A vertical tangent line at x=a

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• a relative maximum at x=a

• a relative minimum at x=a

• no relative extrema at x=a

• a vertical tangent line at x=a

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find all relative extrema for the function above:

• A

• B

• C

• D

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSA.APR.B.3

For the function above, find all relative extrema.

• A

• B

• C

• D

Tags

CCSS.HSA.REI.D.10

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

when you check for sign changes at the critical points of a function, you are using the

• IVT

• MVT

• 1st Derivative Test

• 2nd Derivative Test

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

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

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down