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Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use the fact that the answer to question 4 is (a) and the correct formula from that problem to answer this ques- tion about a mysterious but invertible and differentiable function f(x). This function passes through the point (2, 4) where the slope of its tangent line is f'(2) = -7. 4. Based on this information, which of the following statements about the inverse function f-l is necessarily true? (a) The graph of y = f-1 passes through the point (4, 2) where its tangent line has a slope of (f-1)' (4) = 1/f"(2) = -1/7. (b) The graph of y = ƒ-l passes through the point (2, 4) where its tangent line has a slope of (f-)' (2) = 1/f'(2) = -1/7. (c) The graph of y = ƒ¯1 passes through the point (2, 4) where its tangent line has a slope of 7. %3D (d) The graph of y = f-1 passes through the point (4, 2) but there is not enough information to determine the slope of its tangent line.
Transcribed Image Text:Use the fact that the answer to question 4 is (a) and the correct formula from that problem to answer this ques- tion about a mysterious but invertible and differentiable function f(x). This function passes through the point (2, 4) where the slope of its tangent line is f'(2) = -7. 4. Based on this information, which of the following statements about the inverse function f-l is necessarily true? (a) The graph of y = f-1 passes through the point (4, 2) where its tangent line has a slope of (f-1)' (4) = 1/f"(2) = -1/7. (b) The graph of y = ƒ-l passes through the point (2, 4) where its tangent line has a slope of (f-)' (2) = 1/f'(2) = -1/7. (c) The graph of y = ƒ¯1 passes through the point (2, 4) where its tangent line has a slope of 7. %3D (d) The graph of y = f-1 passes through the point (4, 2) but there is not enough information to determine the slope of its tangent line.
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