Review

Which of the following statements must be true?

I. f has a relative Min at x=-3.

II. The graph of f has a point of inflection at x=2.

III. The graph of f is concave down for 0 < x < 4.

• I only

• II only

• III only

• I and II only

• I and III only

f has a local Max at x = ?

• -2.314

• -1.332

• 0.350

• 0.829

• 1.234

What are all intervals on which the graph of f is concave down?

• -1 < x < 1

• 0 < x < 2

• 1 < x < 3 ONLY

• -2 < x < -1 ONLY

• -2 < x < -1 AND 1 < x < 3

Let f be a polynomial function with values of f '(x) at selected values of x given in the table. Which of the following must be true for -2 < x < 6 ?

• The graph of f is concave up

• The graph of f has at least two points of inflection

• f is increasing

• f has no critical points

• f has at least two relative extrema

On what intervals is f increasing?

• [-2 , 1] only

• [-2 , 1] and [1 , 3]

• [3 , 5] only

• [0 , 1.5] and [3 , 5]

• [-2 , -1] , [1 , 2], and [4 , 5]

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

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

Find the second derivative of the polynomial...

• 18x + 4

• 9x² + 4x

• 9x + 6

• 12x + 4

Find the second derivative of the polynomial...

• 16 - 8x^-3

• 16 + 8x^-3

• 8 - 4x^-2

• 16 + 8x^-2

Find the second derivative of the polynomial...

• 16 - 8x^-3

• 16 + 8x^-3

• 8 - 4x^-2

• 16 + 8x^-2

Find the second derivative of the polynomial...

• 4x - 5

• 4x

• 4

• 4x - 6