Second Derivative Test

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

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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

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)

Identify the interval from the derivative graph where the function is concave down

• (-1,1) & (3,4)
• (-2,4)
• (-3,-1) & (1,3)
• (-2,1) & (1,4)

Which of the following statements must be true?

I. f has a relative Min at x=-3.

II. The graph of f has a point of inflection at x=2.

III. The graph of f is concave down for 0 < x < 4.

• I only

• II only

• III only

• I and II only

• I and III only

Let f be a polynomial function with values of f '(x) at selected values of x given in the table. Which of the following must be true for -2 < x < 6 ?

• The graph of f is concave up

• The graph of f has at least two points of inflection

• f is increasing

• f has no critical points

• f has at least two relative extrema

Which of the following must be true?

• f is increasing on the interval (0 , 2).

• f is decreasing on the interval (0 , 2).

• f has a local Max at x = 1.

• f has a point of inflection at x = 1.

• The graph of f changes concavity in the interval (0 , 2).

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

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5