Curve Sketching

If f '(3) = 0 and f"(3) < 0, then which of the following must be true?

• There is a local max at x=3
• There is a local min at x = 3
• There is an inflection point at x = 3
• There is an x-intercept at x = 3

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSF.LE.B.5

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

• increasing
• decreasing
• concave up
• concave down

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down

When is a function concave up?

• f"(c)<0
• f'(c)<0
• f"(c)>0
• f'(c)>0

Tags

CCSS.HSF.IF.B.4

When is a function concave down?

• f"(c)<0
• f'(c)<0
• f"(c)>0
• f'(c)>0

Tags

CCSS.HSF.IF.B.4

Where do you find intervals where a function is increasing?

• f'(x)>0
• f"(x)>0
• f'(x)<0
• f"(x)<0

What is a point of inflection?

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

How do you find the critical numbers of a function?

• f'(x) = 0
• f'(x) = 0 and where f'(x) is undefined
• f(x) = 0
• f"(x) =  0