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5. Find the slope of the normal line to f(x) = 3sinx at x = 0 A. In(3) B. –In(3) C. 1/ In(3) D. –1/ln(3) E. O F. None of the above

5. Find the slope of the normal line to f(x) = 3sinx at x = 0 A. In(3) B. –In(3) C. 1/ In(3) D. –1/ln(3) E. O F. None of the above

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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**Problem 5: Slope of the Normal Line to a Function** Given the function \( f(x) = 3^{\sin x} \), find the slope of the normal line to this function at \( x = 0 \). ### Options - A. \(\ln(3)\) - B. \(-\ln(3)\) - C. \(1/\ln(3)\) - D. \(-1/\ln(3)\) - E. 0 - F. None of the above ### Explanation: To find the slope of the normal line, first determine the derivative of the function to find the slope of the tangent line. Then, use the negative reciprocal of the tangent slope to find the slope of the normal line at the given point.
Transcribed Image Text:**Problem 5: Slope of the Normal Line to a Function** Given the function \( f(x) = 3^{\sin x} \), find the slope of the normal line to this function at \( x = 0 \). ### Options - A. \(\ln(3)\) - B. \(-\ln(3)\) - C. \(1/\ln(3)\) - D. \(-1/\ln(3)\) - E. 0 - F. None of the above ### Explanation: To find the slope of the normal line, first determine the derivative of the function to find the slope of the tangent line. Then, use the negative reciprocal of the tangent slope to find the slope of the normal line at the given point.
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