qapmc-5.4 first derivative test

Over what interval(s) is f(x) increasing?

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

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

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.

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)

• (-∞, -√3) ∪ (0, √3)

• (-1, 1)

• (-√3, 0) ∪ (√3, ∞)

At what x-value(s) does f(x) have a minimum?

• x = -3
• x = 1
• x = 5
• x = -3 and x = 5

True or false: all critical points are extrema

• True

• False

• A relative maximum at x=a

• A relative minimum at x=a

• No relative extrema at x=a

• A vertical tangent line at x=a

• 0; -5

• -5; 0

• 2; -1

• -1; 2

What is the relative maximum?

f(x) = x³ - 3x² - 1

• (0,-1)

• (-1,-5)

• (2,-5)

• (5,49)

At what x-value(s) does f(x) have a maximum?

• x = -1
• x = 1
• x = 3
• x = -1 and x = 3