The Second Derivative and Concavity

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

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

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

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

On what interval(s) is the function
y = x^3 + 6x^2
concave down?

• (-∞,-4)
• (-∞,-2)
• (-2,∞)
• (0,∞)

Where is the point of infection for the function y = x^3 + 6x^2?

• 0
• -4
• -2
• 4

On what interval(s) is the function
y = x^3 + 6x^2
concave up?

• (-∞,∞)
• (-∞,-2)
• (-2,∞)
• (0,∞)