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

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,∞)

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 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