47-50. Level curves Consider the paraboloid f(x, y) = 16. - x² - y 2 4 16 and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. 47. f(x, y) = 0; P(0, 16) 48. f(x, y) = 0; P(8, 0)

47-50. Level curves Consider the paraboloid f(x, y) = 16. - x² - y 2 4 16 and the point P on the given level curve of f. Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. 47. f(x, y) = 0; P(0, 16) 48. f(x, y) = 0; P(8, 0)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 92E

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