AP Calculus AB FRQ Questions
AP Calculus AB FRQ Questions
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.
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2.
 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) = x^{2} – 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. __________________________ b. What is the meaning of T'(8)? __________________________

7.  Find the values of m and b that make the following function differentiable. __________________________ 
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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 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.
 Find all values of x where the graph of g has a critical value.
 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.
 On what intervals is the graph of g concave down? Justify your answer.
 Write an equation for the tangent line to the graph of g at the point where x = 3.
 Does this tangent line lie above or below the graph at this point? Justify your answer.