Concavity and the 2nd Derivative

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

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

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• increasing
• decreasing
• concave up
• concave down

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

• increasing
• decreasing
• concave up
• concave down

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

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

Find the x-coordinate of the inflection point of f(x)=6x²-x³.

• -2
• 0
• 2
• None

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, ∞)

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)

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression