AP Calculus AB FRQ Questions

profilekevin_kim212
calcfrq.docx
Home>Mathematics homework help>Calculus homework help>AP Calculus AB FRQ Questions

SHOW ALL WORK AND CALCULATIONS

1. 

Use the graph below to list the x value(s) where the limits as x approaches from the left and right of those integer values(s) are not equal.

A graph is shown beginning at the open point negative two comma negative four continuing to the open point negative one negative one up to a maximum at zero comma zero and back down to the open point one comma negative one. The graph begins again at the closed point one comma two and then condinues down to infinity along the asymptote x equals three then from negative infinity along the asymptote of x equals three the graph increases to the closed point five comma zero. A noncontinuous closed point exists at negative one comma negative two.

__________________________

2.

 

Find limit as x approaches 4 of the quotient of the quantity the square root of the quantity 3 times x plus 4 minus the square root of 4 times x and the quantity x squared minus 4 times x . You must show your work or explain your work in words.

__________________________

3. 

Find limit as x approaches 4 from the left of the quotient of the absolute value of the quantity x minus 4, and the quantity x minus 4 . You must show your work or explain your work in words.

__________________________

4. 

A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2 + 350.

What is the velocity of the ball after 2 seconds?

Include units in your answer.

__________________________

5. 

The cost in dollars of producing x units of a particular telephone is C(x) = x2 - 2500. (10 points)

1. Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 103. Include units in your answer.

2. Find the instantaneous rate of change of C with respect to x when x = 100. Include units in your answer.

__________________________

6. 

The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours.

a. Estimate the value of T'(8). Give units in your answer.

__________________________

b. What is the meaning of T'(8)?

__________________________

t

0

2

4

6

8

10

12

14

T

73

73

70

68

73

80

86

89

7. 

Find the values of m and b that make the following function differentiable.

the piecewise function f of x equals x squared when x is less than or equal to two or mx plus b when x is greater than two

__________________________

8. 

Find f'(x) for f(x) = cos2(3x3).

__________________________

9. 

Find f'(x) for f(x) = ln(x2 + e3x). 

__________________________

10. 

Find dy dx by implicit differentiation for ysin(x) = xsin(y).

__________________________

11. Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=${x^2–16}/{x−2}$, with x ≠ 2.

a) Find all values of x where the graph of g has a critical value. 

b) For each critical value, state whether the graph of g has a local maximum, local minimum or neither. You must justify your answers with a complete sentence. 

c) On what intervals is the graph of g concave down? Justify your answer. 

d) Write an equation for the tangent line to the graph of g at the point where x = 3. 

e) Does this tangent line lie above or below the graph at this point? Justify your answer.