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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
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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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.
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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