AP Calculus AB Multiple Choice

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1. 

Use the graph of f(x) below to estimate the value of f '(-2):

Graph is an inverted parabola with x-intercepts at x equals negative 3 and positive 3 and y-intercept at y = 9. (4 points)

 

-1

0

1

4

2. 

Given the graph of f '(x), the derivative of f(x), which of the following statements are true about the graph of f(x)? (4 points)

Graph is parabola with x-intercepts at x equals 0 and 3 and vertex at x = 1

I.The graph of f has a critical point at x = 0. II.The graph of f has a critical point at x = 1. III.The graph of f has a point of inflection at x = 1.

 

I only

II only

III only

I and III only

3. 

Find the critical point of the function f(x) = -x2 + 4x - 5. (4 points)

 

(2, -1)

(2, 0)

(-2, -37)

(2, 1)

4. 

For what values of x is the graph of y equals negative 3 divided by the quantity 4 plus x concave downward? (4 points)

 

x > 4

x < -4

x > -4

No values of x

5. 

At what value(s) of x does f(x) = x4 - 18x2 have a critical point where the graph changes from decreasing to increasing? (4 points)

 

0 and -3 only

0 and 3 only

-3, and 3 only

0 only