Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where a, b and c are real numbers. It is given that the tangent plane to the graph of f at the point (-1, 3, f(−1, 3)) has equation z =-6x-y-3. a) Explain why the information given tells you that f(-1,3) = 0. b) Consider the contour line of the function f through the point (-1, 3) in the (x, y)-plane. Find the equation of the tangent line to this contour line at the point (-1, 3). You do not need to find the values for a, b and c to answer this question! c) Find the values for the numbers a, b and c.

A function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where a, b and c are real numbers. It is given that the tangent plane to the graph of f at the point (-1, 3, f(−1, 3)) has equation z =-6x-y-3. a) Explain why the information given tells you that f(-1,3) = 0. b) Consider the contour line of the function f through the point (-1, 3) in the (x, y)-plane. Find the equation of the tangent line to this contour line at the point (-1, 3). You do not need to find the values for a, b and c to answer this question! c) Find the values for the numbers a, b and c.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
A function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where a, b and c are real numbers. It is given that the tangent plane to the graph off at the point (−1, 3, ƒ(−1, 3)) has equation z = -6x-y-3. a) Explain why the information given tells you that f(-1, 3) = 0. b) Consider the contour line of the function f through the point (-1, 3) in the (x, y)-plane. Find the equation of the tangent line to this contour line at the point (-1, 3). You do not need to find the values for a, b and c to answer this question! c) Find the values for the numbers a, b and c.
Transcribed Image Text:A function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where a, b and c are real numbers. It is given that the tangent plane to the graph off at the point (−1, 3, ƒ(−1, 3)) has equation z = -6x-y-3. a) Explain why the information given tells you that f(-1, 3) = 0. b) Consider the contour line of the function f through the point (-1, 3) in the (x, y)-plane. Find the equation of the tangent line to this contour line at the point (-1, 3). You do not need to find the values for a, b and c to answer this question! c) Find the values for the numbers a, b and c.
Expert Solution
steps

Step by step

Solved in 4 steps with 8 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS