Suppose f(x, y) = x²-y-2 (a) On your solution sheet, draw contours of the function z=f(x,y) corresponding to z = −2, −4, −6. Clearly label the axes, and the scale along each axis. Indicate clearly which contour curve is associated with which z value. (b) Find the gradient vector Vƒ(√2, 0). Draw this gradient vector on the contour diagram you sketched for part (a). (c) What is the maximum rate of change of the function at the point (√2, 0)? Enter your answer in the blank below. Round your answer to two decimal places.
Suppose f(x, y) = x²-y-2 (a) On your solution sheet, draw contours of the function z=f(x,y) corresponding to z = −2, −4, −6. Clearly label the axes, and the scale along each axis. Indicate clearly which contour curve is associated with which z value. (b) Find the gradient vector Vƒ(√2, 0). Draw this gradient vector on the contour diagram you sketched for part (a). (c) What is the maximum rate of change of the function at the point (√2, 0)? Enter your answer in the blank below. Round your answer to two decimal places.
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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Please answer this homework problem ASAP
![Suppose f(x, y) = x² - y − 2
= −x² —
-
(a) On your solution sheet, draw contours of the function z=f(x,y) corresponding to
z=−2, -4, -6. Clearly label the axes, and the scale along each axis.
Indicate clearly which contour curve is associated with which z value.
(b) Find the gradient vector Vƒ(√√2, 0). Draw this gradient vector on the
contour diagram you sketched for part (a).
(c) What is the maximum rate of change of the function at the point (√2,0)?
Enter your answer in the blank below. Round your answer to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdae95b20-f352-4f8b-803d-97224dd3d896%2F8ce3c12e-6f95-461f-8ddc-ae4f43e25d99%2Fme9een4_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose f(x, y) = x² - y − 2
= −x² —
-
(a) On your solution sheet, draw contours of the function z=f(x,y) corresponding to
z=−2, -4, -6. Clearly label the axes, and the scale along each axis.
Indicate clearly which contour curve is associated with which z value.
(b) Find the gradient vector Vƒ(√√2, 0). Draw this gradient vector on the
contour diagram you sketched for part (a).
(c) What is the maximum rate of change of the function at the point (√2,0)?
Enter your answer in the blank below. Round your answer to two decimal places.
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