concavity and the second derivative test

concavity

• both concave up and down

• concave down only

• concave up only

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

• no extrema.

• a minimum.

• a maximum.

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

• It's negative

• It's positive

• It's zero

• Cannot be determined

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

• (-3, 1)

• (-∞,-3) U (1, ∞)

• (-5, 0)U(2, ∞)

Over what intervals will the second derivative of f(x) be negative?

• (−∞,−1)

• (−∞,1)

• (1,∞)

• (−1,1)

What will the zeros of the second derivative of f(x) be?

• 4 and 0

• 1 and 2

• -1 and 2

• 0 and 2

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