sketching the curve

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

What is a point of inflection?

• When a function goes from increasing to decreasing.

• When the concavity changes.

• When the derivative changes.

• When the function crosses the x-axis.

How do you find the critical numbers of a function?

• Critical numbers only occur when f'(x) = 0.

• Critical numbers only occur when f'(x) is undefined.

• Critical numbers occur when f'(x) = 0 or where f'(x) is undefined.

• Critical numbers occur as x-intercepts on the graph.

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

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

• increasing
• decreasing
• concave up
• concave down

Where is the point of infection for the function y = x³ + 6x²?

• 0

• -4

• -2

• 4

Tags

CCSS.HSF-IF.C.7C

On what interval(s) is the function y=x³ + 6x²

concave down?

• (-∞,-4)

• (-∞,-2)

• (-2,∞)

• (0,∞)

Let f be the function given by f(x) = x³. What are all values of c that satisfy the conclusion of the Mean Value Theorem on the open interval (-1, 2)?

• 0 only

• 1 only

• √3 only

• -1 and 1

Let g(x) = (1/4)x⁴-4x³+24x², for what values of x does the graph of g have points of inflection?

• x = -3 
• x = 0
• x = 4
• g has no points of inflection