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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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