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1. For function z = f(x, y) where f(x, y) = 4 – x² – 2y², we compute that fa(1,1) = -2 and fy(1,1) = -4. In our class, we have learned that the partial derivative fæ (1, 1) determines a tangent line L1 of graph z = the line L1 can be described by a system of two equations f(x, y) at (1, 1,1). In particular, z – 1= -2(x – 1), = 1. Similarly, fy(1, 1) determines one other tangent line L2 of graph z = f(x, y) at (1, 1, 1), which can be described by [2 -1= -4(y – 1), x = 1. a) Write the vector equations of L1 and L2, respectively. Specifically, describe the equation of L1 as 7 = ĩo + tủi for some v1, where ro = similar argument to describe the equation of L2 as = ro+ td2 for some v2. (1, 1, 1). Use a b) Use the previous solution, compute the scalar equation of the plane that contains both Lị and L2.

1. For function z = f(x, y) where f(x, y) = 4 – x² – 2y², we compute that fa(1,1) = -2 and fy(1,1) = -4. In our class, we have learned that the partial derivative fæ (1, 1) determines a tangent line L1 of graph z = the line L1 can be described by a system of two equations f(x, y) at (1, 1,1). In particular, z – 1= -2(x – 1), = 1. Similarly, fy(1, 1) determines one other tangent line L2 of graph z = f(x, y) at (1, 1, 1), which can be described by [2 -1= -4(y – 1), x = 1. a) Write the vector equations of L1 and L2, respectively. Specifically, describe the equation of L1 as 7 = ĩo + tủi for some v1, where ro = similar argument to describe the equation of L2 as = ro+ td2 for some v2. (1, 1, 1). Use a b) Use the previous solution, compute the scalar equation of the plane that contains both Lị and L2.

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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f (x, y) where f(x, y) = 4 – x² – 2y², we compute that fæ(1, 1) = 1. For function z = -2 and fy(1,1) = -4. In our class, we have learned that the partial derivative fa(1, 1) determines a tangent line L1 of graph z = f (x, y) at (1, 1, 1). In particular, the line L1 can be described by a system of two equations 1 = -2(x – 1), - Z y = 1. Similarly, fy(1, 1) determines one other tangent line L2 of graph z = (1,1, 1), which can be described by f(x, y) at z – 1 = -4(y – 1), x = =1. a) Write the vector equations of L1 and L2, respectively. Specifically, describe the equation of L1 as 7 = ro + tủi for some v1, where ro = (1, 1, 1). Use a similar argument to describe the equation of L2 as = ro+ tū2 for some 02. b) Use the previous solution, compute the scalar equation of the plane that contains both Lị and L2.
Transcribed Image Text:f (x, y) where f(x, y) = 4 – x² – 2y², we compute that fæ(1, 1) = 1. For function z = -2 and fy(1,1) = -4. In our class, we have learned that the partial derivative fa(1, 1) determines a tangent line L1 of graph z = f (x, y) at (1, 1, 1). In particular, the line L1 can be described by a system of two equations 1 = -2(x – 1), - Z y = 1. Similarly, fy(1, 1) determines one other tangent line L2 of graph z = (1,1, 1), which can be described by f(x, y) at z – 1 = -4(y – 1), x = =1. a) Write the vector equations of L1 and L2, respectively. Specifically, describe the equation of L1 as 7 = ro + tủi for some v1, where ro = (1, 1, 1). Use a similar argument to describe the equation of L2 as = ro+ tū2 for some 02. b) Use the previous solution, compute the scalar equation of the plane that contains both Lị and L2.
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