Find the point on the paraboloid zy²= + that is closest to the point (3, 0, 0).425Hint: Let (x, y, z) be a point on the paraboloid. The distance D between (x, y, z) and the fixedpoint (3,0,0) is √√(x − 3)² + y² + z². Note that D is minimum if and only if D² is minumum.Use Lagrange multiplier.

We need to find the point on the paraboloid , that is closest to the point .

Answered: Find the point on the paraboloid z = +…

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Find the point on the paraboloid z = + 4 | 25 that is closest to the point (3, 0, 0).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 32E

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Question

Find the point on the paraboloid z
y²
= + that is closest to the point (3, 0, 0).
4
25
Hint: Let (x, y, z) be a point on the paraboloid. The distance D between (x, y, z) and the fixed
point (3,0,0) is √√(x − 3)² + y² + z². Note that D is minimum if and only if D² is minumum.
Use Lagrange multiplier.

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Step 1: Introduction

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Step 2: Identifying Lagrangian function

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Step 3: Calculating first order condition of constrained optimization

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Step 4: Identifying critical points

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Step 5: Calculating minimum distance

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