Find the point(s) on the cone z² = x² + y² closest to the point (1,2,0) a) What function needs to be minimized? b) Set up your distance formula for the points (x,y,z) to (1, 2, 0) (this will be f(x,y,z) c) g(x,y,z) = (think g(x,y,z) = 0 using cone equation) d) Find the various partials and set up Vf Avg (show equivalence for each partial w/respect to x, y, and z): e) There should be an obvious one for solving for λ and a variable: f) Subst into cone equation to solve and get at least one point: g) Subst A into 2 partial deriv equations to solve for other variables: h) Use candidates test to find minimum distance/closest point(s)
Find the point(s) on the cone z² = x² + y² closest to the point (1,2,0) a) What function needs to be minimized? b) Set up your distance formula for the points (x,y,z) to (1, 2, 0) (this will be f(x,y,z) c) g(x,y,z) = (think g(x,y,z) = 0 using cone equation) d) Find the various partials and set up Vf Avg (show equivalence for each partial w/respect to x, y, and z): e) There should be an obvious one for solving for λ and a variable: f) Subst into cone equation to solve and get at least one point: g) Subst A into 2 partial deriv equations to solve for other variables: h) Use candidates test to find minimum distance/closest point(s)
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:Find the point(s) on the cone z² = x² + y² closest to the point (1,2,0)
a) What function needs to be minimized?
b) Set up your distance formula for the points (x,y,z) to (1, 2, 0) (this will be f(x,y,z)
c) g(x,y,z) =
(think g(x,y,z) = 0 using cone equation)
d) Find the various partials and set up Vf Avg (show equivalence for each partial
w/respect to x, y, and z):
e) There should be an obvious one for solving for λ and a variable:
f) Subst into cone equation to solve and get at least one point:
g) Subst A into 2 partial deriv equations to solve for other variables:
h) Use candidates test to find minimum distance/closest point(s)
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