First And Second Derivative

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

Use the sign chart for f'(x).  There is(are) ...

• a local maximum at x = -2.
• a local minimum at
  x = -2 and a local maximum at x = 4.
• a local maximum at
  x = -2 and a local minimum at x = 4.
• no extrema.

On what interval(s) is the function
concave up?

 $y=x^3+6x^2$  

• (-∞,∞)

• (-∞,-2)

• (-2,∞)

• (0,∞)

At which point is f ' (x) <0 and f''(x) >0?

• A

• C

• E

• F

• G

The graph of y = f ' (x) is shown. What is (are) the x location(s) of the point of inflection on f(x) ?

• x = -1 only

• x = -3 and x = 0.5

• x = -3 and x = 2

• x = 2 only

If f ' (x) goes from increasing to decreasing at x = c, then f(c)

• Is a relative Maximum

• Is a relative Minimum

• Is concave up

• is a point of inflection.

Suppose f ' (3) = 0, and f '' (3) =5. Which of the following is (are) true? Choose all that apply.

• f(x) is concave up at x = 3

• f(3) Is a critical point.

• f(3) is a relative Maximum value

• f(3) is a relative Minimum Value

• x = 3 is the location of a point of inflection.