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# AP Calculus January 5, 2009

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Pre-test on applications of derivatives.

Pre-test on applications of derivatives.

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• 1. Applications of Derivatives ... Pre-Test Calculus Studies
• 2. The graph of the function is increasing on which of the following intervals? I 1<x II 0 < x < 1 III x < 0 (A) I only (B) II only (C) III only (D) I and II only (E) I and III only
• 3. Let: For how many inputs c between a = -2 and b = 2 is it true that
• 4. The table below gives some values of the derivative of a function g. Based on this information it appears that on the interval covered by the table (A) g is increasing and concave up everywhere (B) g is increasing and concave down everywhere (C) g has a point of inﬂection (D) g is decreasing and concave up everywhere (E) g is decreasing and concave down everywhere
• 5. Suppose ƒ is a continuous and differentiable function on the interval [0, 1] and g(x) = ƒ(3x). The table below gives some values of ƒ. What is the approximate value of g'(0.1)? (A) 3.80 (B) 3.84 (C) 3.88 (D) 3.92 (E) 3.96
• 6. If has a local minimum at x = 4 then the value of k is: (A) -1 (B) (C) 1 (D) 4 (E) None of these
• 7. Let ƒ be a function given by (a) Find the domain of ƒ. (b) On the graph below, sketch the graph of ƒ.
• 8. (c) Write an equation for each horizontal asymptote of the graph of ƒ. (d) Find the range of ƒ. [Use to justify your answer.]