Consider the parabola given by y = x² + 1. a) Use Lagrange's method to find the point on the parabola which is closest to the origin (hint: use the distance-squared function f(x, y) x² + y?). %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 36E
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Consider the parabola given by y = x² + 1.
a) Use Lagrange's method to find the point on the parabola which is
closest to the origin (hint: use the distance-squared function f(x, y) :
x² + y?).
%3D
b) Consider now the portion of the parabola which is below the line
y = 2. Which points have the largest distance from the origin in this case?
Try to explain this situation from the point of view of Lagrange's
method.
Transcribed Image Text:Consider the parabola given by y = x² + 1. a) Use Lagrange's method to find the point on the parabola which is closest to the origin (hint: use the distance-squared function f(x, y) : x² + y?). %3D b) Consider now the portion of the parabola which is below the line y = 2. Which points have the largest distance from the origin in this case? Try to explain this situation from the point of view of Lagrange's method.
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