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

On which interval is this function increasing?

• −2.5 < x < 2.5
• 0 < x < 5
• 0 < x < 55
• −5 < x < 0

Tags

CCSS.HSF.IF.B.4

CCSS.HSA.REI.D.10

CCSS.HSF.IF.C.7

On what interval is this function increasing?

• x ≤ 1
• x ≥ 1
• y ≤ −4
• y ≥ −4

Tags

CCSS.HSG.SRT.C.8

On what interval is this function increasing?

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

Tags

CCSS.HSG.SRT.C.8

The graph shown is the DERIVATIVE of f. From the derivative's graph, identify the interval graph where f (the original function) is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)

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

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