AP CALC 4.1-4.4 Quiz Review

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

• increasing
• decreasing
• concave up
• concave down

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing

Tags

CCSS.HSF.IF.B.4

If a function has a second derivative that is positive, what does that tell you?

• The function is increasing

• The function is decreasing

• The function is concave up

• The function is concave down

Where does the function, f(x) = 2x³ - 9x² + 12x -3 have relative max/min values?

• Rel max x = -1, Rel min x = 2

• Rel min x = 1, Rel min x = 2

• Rel max x = 1, Rel min x = 2

• Rel max x = 2, Rel min x = 1

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

• an inflection point
• a critical point
• a minimum
• a maximum

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

• 0
• -1
• 2
• 5

Tags

CCSS.HSA.APR.B.3

What is a point of inflection?

• When a function goes from increasing to decreasing
• When a function goes from concave up to concave down

Find the x-coordinate of the inflection point of f(x)=6x²-x³.

• -2
• 0
• 2
• None

How many extrema are in the picture?

• 2
• 3
• 4
• 5

Tags

CCSS.HSA.APR.B.3

If f"(x) < 0, what is true about f(x)?

• it is concave up there

• it has an inflection point

• It's zero

• it is concave down there