I need help on this question please. The answers in the red are wrong and the answers with the red "x" to the side of it are also wrong. Thank you in advance!! The problem involves finding the critical point and evaluating the discriminant for the function \( f(x, y) = (4x^2 - y)(x^2 + y) \).(a) Find the critical point of \( f(x, y) \).- The critical point is given by \( (x, y) = (0,0) \).(b) Find the discriminant, \( D(x, y) \), for the function.- The value of the discriminant at the critical point is \( D = 0 \).The question asks, "What does this tell us about the critical point?" The options given in a dropdown include "The critical point is a local maximum," but this choice is incorrect.(c) Sketch contours near the critical point to determine, or confirm, whether it is a local maximum, a local minimum, a saddle point, or none of these. The dropdown option states "The discriminant doesn't tell us anything," which is incorrect. (a) Find the critical point of the function \( f(x, y) = (4x^2 - y)(x^2 + y) \).The critical point is found at:\[ (x, y) = (0, 0) \](b) Find the discriminant, \( D(x, y) \), for the function.The discriminant is:\[ D(x, y) = (0, 0) \]What is the value of the discriminant at the critical point?The value of the discriminant is:\[ D = 0 \]The provided options prompt the user to determine or confirm whether the critical point is a local maximum, local minimum, or saddle point. An information box provides options and indicates:- The critical point is a local maximum.- The critical point is a local minimum.- The critical point is a saddle point.- The discriminant doesn’t tell us anything.The selected option is:✓ The discriminant doesn’t tell us anything.

Answered: Image /qna-images/answer/c6e35e0d-3d80-4115-b86f-68befa0e8b0e.jpg

(a) Find the critical point of f(x, y) = (4x² − y) (x² + y). (x, y) = (0,0) (b) Find the discriminant, D(x, y) for the function. D(x, y) = (0,0) what is the value of the discriminant at the critical point? D = 0 What does this tell us about the critical point? The critical point is a local maximum Ⓒ (c) Sketch contours near the critical point to determine, or confirm, whether it is a local maximum, a local minimum, a saddle point, or none of these. The discriminant doesn't tell us anything

(a) Find the critical point of f(x, y) = (4x² − y) (x² + y). (x, y) = (0,0) (b) Find the discriminant, D(x, y) for the function. D(x, y) = (0,0) what is the value of the discriminant at the critical point? D = 0 What does this tell us about the critical point? The critical point is a local maximum Ⓒ (c) Sketch contours near the critical point to determine, or confirm, whether it is a local maximum, a local minimum, a saddle point, or none of these. The discriminant doesn't tell us anything

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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