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(1) Values of z = f(x, y) and its derivatives are given in the table below und reans contour diagram is to the right (contours are labelled, but for reference, the dashed contours are even and dark contours are odd). Use them to answer the following questions. Make sure to justify all your work. 1.5 1.0 (x, y) f fx fy fax fyy fry (0,0) 0 und und und und und 0.5 -3 (1,0) =4 0 1 -1 2 (1, 1) 5.5 2 =1 1 1 ત્યાર (1,-1) 5.5 1 2 1 0.0 મુ ક ા માની શ (0, 1) -6 0 -1 #1 1 2 (-1,1) -5.5 -1 -2 1 2 1 (-1,0) 0 0 1 1 2 -0.5 (0, -1) -6 0 1 1 2 1 (-1,-1) -5.5 1 2 =1 #1 2 -1.0 (a) Identify which of the points in the table are critical points. -1.5 -1.0 -0.5 10.0 0.5 1.0 1.5 (b) Classify the critical points appearing in the table as minima, maxima or neither. Provide reasoning for each. (c) Find an equation for the tangent plane to f(x, y) at the point (1,-1). Write your answer in the form ax+by+cz = d. subiect to the constraint

(1) Values of z = f(x, y) and its derivatives are given in the table below und reans contour diagram is to the right (contours are labelled, but for reference, the dashed contours are even and dark contours are odd). Use them to answer the following questions. Make sure to justify all your work. 1.5 1.0 (x, y) f fx fy fax fyy fry (0,0) 0 und und und und und 0.5 -3 (1,0) =4 0 1 -1 2 (1, 1) 5.5 2 =1 1 1 ત્યાર (1,-1) 5.5 1 2 1 0.0 મુ ક ા માની શ (0, 1) -6 0 -1 #1 1 2 (-1,1) -5.5 -1 -2 1 2 1 (-1,0) 0 0 1 1 2 -0.5 (0, -1) -6 0 1 1 2 1 (-1,-1) -5.5 1 2 =1 #1 2 -1.0 (a) Identify which of the points in the table are critical points. -1.5 -1.0 -0.5 10.0 0.5 1.0 1.5 (b) Classify the critical points appearing in the table as minima, maxima or neither. Provide reasoning for each. (c) Find an equation for the tangent plane to f(x, y) at the point (1,-1). Write your answer in the form ax+by+cz = d. subiect to the constraint

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter10: Radical Functions And Equations
Section: Chapter Questions
Problem 15CT
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(1) Values of z = f(x, y) and its derivatives are given in the table below und reans contour diagram is to the right (contours are labelled, but for reference, the dashed contours are even and dark contours are odd). Use them to answer the following questions. Make sure to justify all your work. 1.5 1.0 (x, y) f fx fy fax fyy fry (0,0) 0 und und und und und 0.5 -3 (1,0) =4 0 1 -1 2 (1, 1) 5.5 2 =1 1 1 ત્યાર (1,-1) 5.5 1 2 1 0.0 મુ ક ા માની શ (0, 1) -6 0 -1 #1 1 2 (-1,1) -5.5 -1 -2 1 2 1 (-1,0) 0 0 1 1 2 -0.5 (0, -1) -6 0 1 1 2 1 (-1,-1) -5.5 1 2 =1 #1 2 -1.0 (a) Identify which of the points in the table are critical points. -1.5 -1.0 -0.5 10.0 0.5 1.0 1.5 (b) Classify the critical points appearing in the table as minima, maxima or neither. Provide reasoning for each. (c) Find an equation for the tangent plane to f(x, y) at the point (1,-1). Write your answer in the form ax+by+cz = d. subiect to the constraint
Transcribed Image Text:(1) Values of z = f(x, y) and its derivatives are given in the table below und reans contour diagram is to the right (contours are labelled, but for reference, the dashed contours are even and dark contours are odd). Use them to answer the following questions. Make sure to justify all your work. 1.5 1.0 (x, y) f fx fy fax fyy fry (0,0) 0 und und und und und 0.5 -3 (1,0) =4 0 1 -1 2 (1, 1) 5.5 2 =1 1 1 ત્યાર (1,-1) 5.5 1 2 1 0.0 મુ ક ા માની શ (0, 1) -6 0 -1 #1 1 2 (-1,1) -5.5 -1 -2 1 2 1 (-1,0) 0 0 1 1 2 -0.5 (0, -1) -6 0 1 1 2 1 (-1,-1) -5.5 1 2 =1 #1 2 -1.0 (a) Identify which of the points in the table are critical points. -1.5 -1.0 -0.5 10.0 0.5 1.0 1.5 (b) Classify the critical points appearing in the table as minima, maxima or neither. Provide reasoning for each. (c) Find an equation for the tangent plane to f(x, y) at the point (1,-1). Write your answer in the form ax+by+cz = d. subiect to the constraint
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