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(c) Is there a value c, for 0

(c) Is there a value c, for 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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(c) Is there a value c, for 0 <c<3, such that g (c) = 2? Justify your answer. Copyright ©2017. The College Board. These materials are part of a College Board program Use or distribution of these materials online or in print beyond your school's participation in the program is prohibited. AP CollegeBoard AP Calculus BC Unit 3 Progress Check: FRQ Part A Please respond on separate paper, following directions from your teacher. Page 1 of 2 ↑ Test Booklet (d) Leth be the function with first derivative given by h' (x) = 4xe. At what value of in the interval 0≤x≤4 does the instantaneous rate of change of h equal the average rate of change of f over the interval 0<<4? Please respond on separate paper, following directions from your teacher.
Transcribed Image Text:(c) Is there a value c, for 0 <c<3, such that g (c) = 2? Justify your answer. Copyright ©2017. The College Board. These materials are part of a College Board program Use or distribution of these materials online or in print beyond your school's participation in the program is prohibited. AP CollegeBoard AP Calculus BC Unit 3 Progress Check: FRQ Part A Please respond on separate paper, following directions from your teacher. Page 1 of 2 ↑ Test Booklet (d) Leth be the function with first derivative given by h' (x) = 4xe. At what value of in the interval 0≤x≤4 does the instantaneous rate of change of h equal the average rate of change of f over the interval 0<<4? Please respond on separate paper, following directions from your teacher.
1. A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f (2) is a real number. -3034 2 f(x) 5 -1 2 7 f' (2) -2 4 0 1 The table above gives values of a twice-differentiable function of and its first derivative f for selected values of *. Let 9 be the function defined by g(x) = ƒ (2x — x²). (a) What is the value of g(-1)? Please respond on separate paper, following directions from your teacher. (b) It is known that g" (0) = 0. What is the value of f" (0)? Please respond on separate paper, following directions from your teacher. Pogo
Transcribed Image Text:1. A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f (2) is a real number. -3034 2 f(x) 5 -1 2 7 f' (2) -2 4 0 1 The table above gives values of a twice-differentiable function of and its first derivative f for selected values of *. Let 9 be the function defined by g(x) = ƒ (2x — x²). (a) What is the value of g(-1)? Please respond on separate paper, following directions from your teacher. (b) It is known that g" (0) = 0. What is the value of f" (0)? Please respond on separate paper, following directions from your teacher. Pogo
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