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1. At the point (1, -1), the function (z,y) has a derivative of b in the direction toward (3, 1) and a derivative of 8 in the direction toward (1, 6). a) Find f.(1, –1) and fy(1, –1), b) Find the derivative of f at (1, –1) in the direction toward the point (-2,4).

1. At the point (1, -1), the function (z,y) has a derivative of b in the direction toward (3, 1) and a derivative of 8 in the direction toward (1, 6). a) Find f.(1, –1) and fy(1, –1), b) Find the derivative of f at (1, –1) in the direction toward the point (-2,4).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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At the point (1,−1), the function (x, y) has a derivative of 5 in the direction toward (3,1) and a derivativeof 8 in the direction toward (1,6).

a) Findfx(1,−1) andfy(1,−1),

b) Find the derivative offat (1,−1) in the direction toward the point (−2,4).

1. At the point (1, -1), the function (z, y) has a derivative of 5 in the direction toward (3, 1) and a derivative of 8 in the direction toward (1,6). a) Find fa(1, –1) and fy(1, –1), b) Find the derivative of f at (1,–1) in the direction toward the point (-2, 4). 2. Find the point closest to the origin on the curve of intersection of the cone 2 = 2r + 2y? and the plane I+y+z= 1. 3. Integrate f(r, y) = over a) The triangle with vertices (0,0), (3, v3) and (3,0) b) the second quadrant of the ry-plane.
Transcribed Image Text:1. At the point (1, -1), the function (z, y) has a derivative of 5 in the direction toward (3, 1) and a derivative of 8 in the direction toward (1,6). a) Find fa(1, –1) and fy(1, –1), b) Find the derivative of f at (1,–1) in the direction toward the point (-2, 4). 2. Find the point closest to the origin on the curve of intersection of the cone 2 = 2r + 2y? and the plane I+y+z= 1. 3. Integrate f(r, y) = over a) The triangle with vertices (0,0), (3, v3) and (3,0) b) the second quadrant of the ry-plane.
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