(a) Find the tangent plane and normal line of the surface f(x, y, z) = x3 + y² – 6z + 5 = 0, at the point Po(1,3,0) (b) Take projection of the above surface on xy plane (fix z=0 in above equation) and then find the directions in which the resulting function f(x.y) increases and decreases most rapidly at Po and then find derivative of the function in these directions.
(a) Find the tangent plane and normal line of the surface f(x, y, z) = x3 + y² – 6z + 5 = 0, at the point Po(1,3,0) (b) Take projection of the above surface on xy plane (fix z=0 in above equation) and then find the directions in which the resulting function f(x.y) increases and decreases most rapidly at Po and then find derivative of the function in these directions.
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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Transcribed Image Text:Question 2.
(a) Find the tangent plane and normal line of the surface
f(x, y, z) = x3 + y² – 6z + 5 = 0, at the point Po(1,3,0)
(b) Take projection of the above surface on xy plane (fix z-0 in above equation) and then
find the directions in which the resulting function f(x.y) increases and decreases most
rapidly at Po and then find derivative of the function in these directions.
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