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AP Calculus Slides December 10, 2007

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Darren Kuropatwa
Darren Kuropatwa

This document contains several calculus practice problems related to applications of derivatives. It includes questions about determining where a function is increasing or decreasing based on its graph, finding values of derivatives from a table, determining concavity from a table of derivatives, approximating derivatives, identifying conditions for local extrema, sketching graphs with horizontal asymptotes, and determining domains and ranges.

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Calculus Studies Applications of Derivatives ... Pre-Test
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
Let: For how many inputs c between a = -2 and b = 2 is it true that
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
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
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
Let ƒ be a function given by (a) Find the domain of ƒ. (b) On the graph below, sketch the graph of ƒ.
(c) Write an equation for each horizontal asymptote of the graph of ƒ. (d) Find the range of ƒ. [Use to justify your answer.]

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AP Calculus Slides December 10, 2007

  • 1. Calculus Studies Applications of Derivatives ... Pre-Test
  • 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.]