AP Calculus AB FRQ Questions

AP Calculus AB FRQ Questions

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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.

 

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Find  . You must show your work or explain your work in words.

 

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3.  Find  . You must show your work or explain your work in words.

 

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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.

 

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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.

 

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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.

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

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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.

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8.  Find f'(x) for f(x) = cos2(3×3).

 

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9.  Find f'(x) for f(x) = ln(x2 + e3x).

 

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

 

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  1. 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.
  2. Find all values of x where the graph of g has a critical value.
  3. 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.
  4. On what intervals is the graph of g concave down? Justify your answer.
  5. Write an equation for the tangent line to the graph of g at the point where x = 3.
  6. Does this tangent line lie above or below the graph at this point? Justify your answer.

 

 

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