AP Calc AB 3.4-3.6 Quiz

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

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

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• increasing
• decreasing
• concave up
• concave down

Tags

CCSS.HSF-BF.B.4A

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)

Tags

CCSS.HSF.IF.B.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

Where is the point of infection for the function y = x³ + 6x²?

• 0

• -4

• -2

• 4

On what interval(s) is the function y=x³ + 6x²

concave down?

• (-∞,-4)

• (-∞,-2)

• (-2,∞)

• (0,∞)

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

• 100ft x 200ft

• 102ft x 196 ft

• 50 ft x 300 ft

• 50 ft x 175 ft

If y=2x-8, what is the minimum value of the product xy?

• -16
• -8
• -4
• 2

Tags

CCSS.8.EE.C.7B