Homework Help is Here – Start Your Trial Now!
Math
Calculus
Question 3.72) Consider the rotated ellipse x² - xy + y² = 108 shown beside. dy A) Use implicit differentiation to find an expression for dx B) Find the coordinates (x, y) of the points on the ellipse where the tangent line is horizontal.

Question 3.72) Consider the rotated ellipse x² - xy + y² = 108 shown beside. dy A) Use implicit differentiation to find an expression for dx B) Find the coordinates (x, y) of the points on the ellipse where the tangent line is horizontal.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 79E
See similar textbooks
icon
Related questions
Question
Can you please answer question 3.72
Question 3.61) Verify the Mean Value Theorem (find that 'c' that is supposed to exist) for the function f(x)=√x on the interval [0,9]. Question 3.62) Use the corollary to the IVT and Rolle's Theorem to show that the function p(x)=x² - 4x³−8x² +29 has a unique root in the interval (1,4). Question 3.71) Shown beside is a curve called "lemniscate", given by 2(x² + y²)² = 25(x² − y²). A) Use implicit differentiation to obtain that dy x 50-8(x² + y²) dx y 50+8(x² + y²) B) Verify that the point (3,1) belongs to the lemniscate and find the equation of the line tangent to the curve at this point. Question 3.72) Consider the rotated ellipse x² - xy + y² = 108 shown beside. dy A) Use implicit differentiation to find an expression for dx B) Find the coordinates (x, y) of the points on the ellipse where the tangent line is horizontal. -2 Question 3.73) Find the derivative of the following functions, which have x showing both in the base and in the exponent... Simplify when appropriate. A) y=(√x) ¹² B) (In x) x C) (1+¹)*
Transcribed Image Text:Question 3.61) Verify the Mean Value Theorem (find that 'c' that is supposed to exist) for the function f(x)=√x on the interval [0,9]. Question 3.62) Use the corollary to the IVT and Rolle's Theorem to show that the function p(x)=x² - 4x³−8x² +29 has a unique root in the interval (1,4). Question 3.71) Shown beside is a curve called "lemniscate", given by 2(x² + y²)² = 25(x² − y²). A) Use implicit differentiation to obtain that dy x 50-8(x² + y²) dx y 50+8(x² + y²) B) Verify that the point (3,1) belongs to the lemniscate and find the equation of the line tangent to the curve at this point. Question 3.72) Consider the rotated ellipse x² - xy + y² = 108 shown beside. dy A) Use implicit differentiation to find an expression for dx B) Find the coordinates (x, y) of the points on the ellipse where the tangent line is horizontal. -2 Question 3.73) Find the derivative of the following functions, which have x showing both in the base and in the exponent... Simplify when appropriate. A) y=(√x) ¹² B) (In x) x C) (1+¹)*
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS