Section 14.7: Problem 8 Previous Problem Problem List Next Problem ( , The discriminant fxxfyy-fy is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a maximum, a minimum, or neither at the origin by imagining what the surface z = f(x, y) looks like. Be sure that you can explain your reasoning! f(x, y) = x¹y4 The critical point at the origin is ✔✓ ?
Section 14.7: Problem 8 Previous Problem Problem List Next Problem ( , The discriminant fxxfyy-fy is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a maximum, a minimum, or neither at the origin by imagining what the surface z = f(x, y) looks like. Be sure that you can explain your reasoning! f(x, y) = x¹y4 The critical point at the origin is ✔✓ ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Section 14.7: Problem 8
Previous Problem Problem List Next Problem
(
The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a
maximum, a minimum, or neither at the origin by imagining what the surface z = f(x, y) looks like. Be sure that you can explain your reasoning!
f(x, y) = x¹y4
The critical point at the origin is ✓ ?
f(x, y) = 1 - x¹y4
The critical point at the origin is
a local maximum
a local minimum.
neither a local maximum nor a local minimum
f(x, y) = xy4
The critical point at the origin is: ?
f(x, y) = x³y4
The critical point at the origin is: ?
f(x, y) = x³y³
The critical point at the origin is: ?
f(x, y) = x²y6
The critical point at the origin is: ?
#
+
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1891e496-bfbf-466b-873c-2589bc3bd10a%2Fb8e68ca7-6fd7-4379-b885-aad4ef4e4c5a%2Fi52hugb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Section 14.7: Problem 8
Previous Problem Problem List Next Problem
(
The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a
maximum, a minimum, or neither at the origin by imagining what the surface z = f(x, y) looks like. Be sure that you can explain your reasoning!
f(x, y) = x¹y4
The critical point at the origin is ✓ ?
f(x, y) = 1 - x¹y4
The critical point at the origin is
a local maximum
a local minimum.
neither a local maximum nor a local minimum
f(x, y) = xy4
The critical point at the origin is: ?
f(x, y) = x³y4
The critical point at the origin is: ?
f(x, y) = x³y³
The critical point at the origin is: ?
f(x, y) = x²y6
The critical point at the origin is: ?
#
+
+
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)