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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda1ab5de-bf4d-4028-8a6d-57425af6cfb9%2F6889ecd2-170b-473d-95f3-92b0d0a69e4a%2Fk98z7t_processed.png&w=3840&q=75)
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.
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