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7. Find all the relative extrema and saddle point(s) of the function given by f(x, y) = (1 + xy)(x+y).

7. Find all the relative extrema and saddle point(s) of the function given by f(x, y) = (1 + xy)(x+y).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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80 1+x² + y² + 3z²¹ where T 5. Suppose that the temperature at a point (x, y, z) in space is given by T(x, y, z) = is measured in degrees Celcius and x, y, z in meters. In which direction does the temperature increase fastest at the point (1,1,0)? What is the maximum rate of change? 6. Consider the sphere G(x, y, z) = x² + y² + z². 8x6y8z + 24 = 0. (a) Determine the standard equation of the plane tangent to G at the point (1,1,2). (b) Find the parametric equations of the normal line to the sphere G through (1,1,2). 7. Find all the relative extrema and saddle point (s) of the function given by f(x, y) = (1 + xy) (x + y).
Transcribed Image Text:80 1+x² + y² + 3z²¹ where T 5. Suppose that the temperature at a point (x, y, z) in space is given by T(x, y, z) = is measured in degrees Celcius and x, y, z in meters. In which direction does the temperature increase fastest at the point (1,1,0)? What is the maximum rate of change? 6. Consider the sphere G(x, y, z) = x² + y² + z². 8x6y8z + 24 = 0. (a) Determine the standard equation of the plane tangent to G at the point (1,1,2). (b) Find the parametric equations of the normal line to the sphere G through (1,1,2). 7. Find all the relative extrema and saddle point (s) of the function given by f(x, y) = (1 + xy) (x + y).
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