Using calculus, find the equation of the tangent line to the function f(x) = 3 cos x when = 2.2. The equation of this tangent line is y Round your numerical values to at least three decimal places. =
Using calculus, find the equation of the tangent line to the function f(x) = 3 cos x when = 2.2. The equation of this tangent line is y Round your numerical values to at least three decimal places. =
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 Statement:**
Using calculus, find the equation of the tangent line to the function
\[ f(x) = 3 \cos x \]
when \( x = 2.2 \).
The equation of this tangent line is
\[ y = \]
Round your numerical values to at least three decimal places.
**Instructions:**
1. Differentiate the function \( f(x) = 3 \cos x \) to find its derivative.
2. Evaluate the derivative at \( x = 2.2 \) to find the slope of the tangent line.
3. Find the y-coordinate of the function at \( x = 2.2 \).
4. Use the point-slope form of a line, \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point of tangency.
5. Round all values to at least three decimal places to obtain the final equation of the tangent line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54e8c682-be67-4ef0-bd1d-cf8b2e543b76%2F78652836-9a69-4611-9726-aff32a8accda%2Fg4hq5y_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Using calculus, find the equation of the tangent line to the function
\[ f(x) = 3 \cos x \]
when \( x = 2.2 \).
The equation of this tangent line is
\[ y = \]
Round your numerical values to at least three decimal places.
**Instructions:**
1. Differentiate the function \( f(x) = 3 \cos x \) to find its derivative.
2. Evaluate the derivative at \( x = 2.2 \) to find the slope of the tangent line.
3. Find the y-coordinate of the function at \( x = 2.2 \).
4. Use the point-slope form of a line, \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point of tangency.
5. Round all values to at least three decimal places to obtain the final equation of the tangent line.
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