MVT & Concavity Review

What is x-value at which the function below has the same slope as the average rate of change over the indicated interval?
f(x) = x² - 3x - 28,  [-4,7]

• 1.5
• -1.5
• 0.5
• -0.5

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Identify the interval from the derivative graph where the function is concave up.

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Identify the interval from the derivative graph where the function is concave down

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

When f'(x) changes from negative to positive, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Given the following graph of f', the derivative of f. For what x-value does f have a relative minimum?

• x=-1 and x=4
• x=-3
• x=1
• x=3

Tags

CCSS.HSF.IF.B.4

When f'(x) changes from positive to negative, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the intervals of concavity for

f(x) = x² + 2x + 1.

• concave up: (-∞,∞)

• concave down: (-∞,∞)

• concave up: (2, ∞)

  concave down: (-∞,2)

• concave up: (-∞,2)

  concave down: (2, ∞)

 If (a,b) is a local minimum, then what will be true about f'(a)?

• It's positive
• It's negative
• It's zero
• Cannot be determined

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

Over what interval(s) is f(x) concave up? (Be careful this is a graph of f'!)

• (-∞, -3) ∪ (1, ∞)

• (-3, 1)

• (-∞,-3) U (1, ∞)

• (-5, 0)U(2, ∞)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7