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Suppose f(x, y) = x² −y+4 (a) On your solution sheet, draw contours of the function z=f(x,y) corresponding to = 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 Vf (1, 1). 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 (1,1)? Enter your answer in the blank below. Round your answer to two decimal places.

Suppose f(x, y) = x² −y+4 (a) On your solution sheet, draw contours of the function z=f(x,y) corresponding to = 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 Vf (1, 1). 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 (1,1)? 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+4 (a) On your solution sheet, draw contours of the function z=f(x,y) corresponding to = 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 Vf (1, 1). 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 (1,1)? Enter your answer in the blank below. Round your answer to two decimal places.
Transcribed Image Text:Suppose f(x, y) = x² −y+4 (a) On your solution sheet, draw contours of the function z=f(x,y) corresponding to = 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 Vf (1, 1). 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 (1,1)? Enter your answer in the blank below. Round your answer to two decimal places.
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