AP Calculus AB Midterm Review Derivatives

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

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

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

The slope 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

Tags

CCSS.HSF.IF.B.6

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)
• (-∞, -√3) ∪ (0, √3)
• (-1, 1)
• (-√3, 0) ∪ (√3, ∞)

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

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.

Use the sign chart for f'(x).  There is(are) ...

• a local maximum at x = -2.
• a local minimum at
  x = -2 and a local maximum at x = 4.
• a local maximum at
  x = -2 and a local minimum at x = 4.
• no extrema.