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Find the coordinates of the point or point(s) on the curve 2y^2 = 5x + 5 which is (are) closest...

Question:

Find the coordinates of the point or point(s) on the curve {eq}2y^2 = 5x + 5{/eq} which is (are) closest to the origin {eq}(0, 0){/eq}.

Lagrange Multipliers

In Lagrange multipliers, we are given two functions and we use them to find the constraints of a given function with respect to other functions.

Given two functions f(x) and g(x);

Firstly we do;

{eq}\nabla f = \lambda \nabla g {/eq}.

Now using the values of {eq}\lambda {/eq}, we then find g(x) values which we then put in f(x) to get the required values.

Answer and Explanation:

We can write the function as:

f(x) = {eq}x^2+y^2 {/eq} this is the distance function.

g(x) = {eq}2y^2 - 5x - 5=0 {/eq}.

Now firstly to calculate...

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Lagrange Multipliers Method & Examples
Lagrange Multipliers Method & Examples

from Business Calculus: Help & Review

Chapter 10 / Lesson 5
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