Chapter 8 Curve sketching AP cumulative review

On what interval(s) is the function

y = x³ + 6x²

concave up?

• (-∞,∞)

• (-∞,-2)

• (-2,∞)

• (0,∞)

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

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

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.

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.

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

• 0

• -4

• -2

• 4

Tags

CCSS.HSF-IF.C.7C

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

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

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

f' is given, which could be f?

• A
• B
• C

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

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

Does the mean value theorem apply to g on [- 2, 5]

• No, b/c the function is not continuous at x = - 4

• Yes. the function is continuous and differentiable on [-2, 5]