Find the equation of the tangent line to the graph of f(x) 1 at x = -2. x+6

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...
icon
Related questions
icon
Concept explainers
Topic Video
Question

How do I solve this?

**Problem:**

Find the equation of the tangent line to the graph of \( f(x) = \frac{1}{x + 6} \) at \( x = -2 \).

**Solution Approach:**

1. **Find the Derivative:**
   To find the equation of the tangent line, you first need the slope of the tangent line at the given point. The slope is found by taking the derivative of the function \( f(x) \).

2. **Evaluate the Derivative at the Given Point:**
   Substitute \( x = -2 \) into the derivative to find the slope of the tangent line at \( x = -2 \).

3. **Find the Point on the Function:**
   Calculate \( f(-2) \) to find the y-coordinate of the point of tangency on the graph.

4. **Use Point-Slope Form to Find the Equation:**
   Use the point-slope formula for a line, \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point of tangency. Substitute the values to get the equation of the tangent line.
Transcribed Image Text:**Problem:** Find the equation of the tangent line to the graph of \( f(x) = \frac{1}{x + 6} \) at \( x = -2 \). **Solution Approach:** 1. **Find the Derivative:** To find the equation of the tangent line, you first need the slope of the tangent line at the given point. The slope is found by taking the derivative of the function \( f(x) \). 2. **Evaluate the Derivative at the Given Point:** Substitute \( x = -2 \) into the derivative to find the slope of the tangent line at \( x = -2 \). 3. **Find the Point on the Function:** Calculate \( f(-2) \) to find the y-coordinate of the point of tangency on the graph. 4. **Use Point-Slope Form to Find the Equation:** Use the point-slope formula for a line, \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point of tangency. Substitute the values to get the equation of the tangent line.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning