Review 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

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

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

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)

• (0,1)

• (-∞,-1) and (0,1)

• (1,∞) and (-1,0)

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5

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.

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.

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

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

• 0

• -4

• -2

• 4

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

concave down?

• (-∞,-4)

• (-∞,-2)

• (-2,∞)

• (0,∞)