separate sheet. 1. Find the equations of the tangent and normal lines to the curve y= x² + 2x +3 at x =-1. (Note: A normal line is a line perpendicular to the tangent line at the point of tangency.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
icon
Related questions
Topic Video
Question
B. Solve the following problems, Write your solutions and final answers on a
separate sheet.
1. Find the equations of the tangent and normal lines to the curve y = x +
2x +3 at x =-1. (Note: A normal line is a line perpendicular to the tangent
line at the point of tangency.)
2. Find the equation of the tangent line to the curve y = x² – 2x-3 that is
parallel to the line x + y = 1.
3. Find the equation of the tangent line to the curve y = x² – 3x +4 that is
perpendicular to the line x - y = -1.
4. Suppose the function is defined by y = f (x) = x² – x
a. Find the average rate of change of y with respect to x over the interval
[1, 3].
b. Find the instantaneous rate of change of y with respect to x at the point
X = -1.
Transcribed Image Text:B. Solve the following problems, Write your solutions and final answers on a separate sheet. 1. Find the equations of the tangent and normal lines to the curve y = x + 2x +3 at x =-1. (Note: A normal line is a line perpendicular to the tangent line at the point of tangency.) 2. Find the equation of the tangent line to the curve y = x² – 2x-3 that is parallel to the line x + y = 1. 3. Find the equation of the tangent line to the curve y = x² – 3x +4 that is perpendicular to the line x - y = -1. 4. Suppose the function is defined by y = f (x) = x² – x a. Find the average rate of change of y with respect to x over the interval [1, 3]. b. Find the instantaneous rate of change of y with respect to x at the point X = -1.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Chain Rule
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
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning