Calculus Concavity

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

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

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

• increasing
• decreasing
• concave up
• concave down

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

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum

How many extrema are in the picture?

• 2
• 3
• 4
• 5

What are all intervals on which the graph of f is concave down?

• -1 < x < 1

• 0 < x < 2

• 1 < x < 3 ONLY

• -2 < x < -1 ONLY

• -2 < x < -1 AND 1 < x < 3

concavity

• concave up only

• concave down only

• both concave up and down

• none

If f '(3) = 0 and f"(3) < 0, then which of the following must be true?

• There is a local max at x=3
• There is a local min at x = 3
• There is an inflection point at x = 3
• There is an x-intercept at x = 3

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression