1st and 2nd derivative Test

The following graph is f ' (x), which intervals is the graph of f(x) increasing?

• (-∞, -1) (1, ∞)

• (-1, 1)

• (-∞, -1)

• (1, ∞)

The following graph is f ' (x), what value of x is a maximum on f(x)?

• x = -1

• x = 1

The following graph is f '' (x), which interval(s) is the graph of f(x) concave up?

• (-∞, -2) (1, 3)

• (-∞, -2)

• (-2, 1) (3, ∞)

• (3, ∞)

The following graph is f '' (x), which interval(s) is the graph of f(x) concave down?

• (-∞, -2) (1, 3)

• (-∞, -2)

• (-2, 1) (3, ∞)

• (3, ∞)

The following graph is f '' (x), what are ALL the inflection points of f(x)?

• x = -2, 0, 1, 3

• x = -2, 1

• x = 1, 3

• x = -2, 1, 3

The following graph is f ' (x), what value of x is a minimum of f(x)?

• x = -1

• x = 1

Tags

CCSS.HSF-IF.C.7A

The following graph is f ' (x), which intervals is the graph of f(x) decreasing?

• (-∞, -1) (1, ∞)

• (-1, 1)

• (-∞, -1)

• (1, ∞)

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

Tags

CCSS.HSF.IF.B.4

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.

Tags

CCSS.HSA.APR.B.3

At what x-value(s) does f(x) have a minimum?

• x = -3
• x = 1
• x = 5
• x = -3 and x = 5

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7