The Fundamental Theorem of Calculus - Pennsbury School ：微积分基本定理彭斯伯学校的.ppt

AP Multiple Choice Question Given the graph of f’(x), at what point does f(x) have a relative minimum? a) A b) B c) C d) D e) E f’(x) AP Multiple Choice Question If f is a quadratic function, then f’’’(x) is a) 2 b) 2x + c c) 0 d) x e) x + c AP Multiple Choice Question If f(x)= , then what is f’(3)+ F(3) a) 30 b) 36 c) 33 d) 27 e) 24 AP Multiple Choice Question Given f(x)= , which of the following is equal to ? a) 7006.450 b) 3.617 c) 2.176 d) 58244.872 e) 7.389 AP Multiple Choice Question = a) b) c) d) e) AP Free Response f(x) AP Free Response a) Set up an integral to calculate the area of region R, and explain why you do not need to be given the upper bound of the integral to solve it b) Calculate the area of region R without using an integration function on a calculator c) Find the volume of the solid with base R and whose cross sections are circles Works Cited /greenl/courses/105/Antiderivatives/secfund.htm /FundamentalTheoremsofCalculus.html /apc/public/repository/Calculus_SF_Theorem.pdf /Classes/CalcI/MoreVolume.aspx The Fundamental Theorem of Calculus * All names and photographs are copyrights of Pokemon. Table of Contents 1) The Fundamental Theorem of Calculus 2) Table of Contents 3) James Gregory 4) Real World Applications 5) The FTC--An Overview 6) FTC Part 1 7) FTC Part 2 8-9) AP Multiple Choice 10-11) Analytical Example 12-13) Conceptual Example 14-15) Free Response 16-17) Graphing 18-19) Practice Problems 20-24) AP Multiple Choice 25-26) AP Free Response 27) Works Cited James Gregory James Gregory was a Scottish mathematician. He was the youngest of three children to a Scottish minister, and was home-schooled for much of his early life. Gregory attended the University of Padua, and eventually became a professor at the University of St. Andrews and the University of Edinburgh. Among his accomplishments are: invention of the Gregorian telescope, development of a method to calculate the Astronomical Unit, being am