Curve Sketching

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

• increasing
• decreasing
• concave up
• concave down

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

• increasing
• decreasing
• concave up
• concave down

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSF.LE.B.5

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

On what interval is this function increasing?

• [4, ∞)
• [−4, ∞)
• [6, ∞)
• 4 < x < 6

Tags

CCSS.HSF-IF.C.7A

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

What is the minimum x value of y = x³ + 6x²

• -4

• 0

• 12

• 4

On what interval(s) is the function

y = x³ + 6x²

concave up?

• (-∞,∞)

• (-∞,-2)

• (-2,∞)

• (0,∞)

f' is given, which could be f?

• A
• B
• C

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Find the point(s) of inflection for f(x) = 2(x)^1/5 + 3

• None
• x = 0
• x = 0, 2
• x = -2, 0, 2

Tags

CCSS.HSF-IF.C.7D