# Help with Lagrange multiplier Problems

• Oct 16th 2009, 08:38 PM
messianic
Help with Lagrange multiplier Problems
Can someone help me on the following Lagrange multiplier problems:

1.) Find the points of the parabola y = (x-1)^2 that are closest to the origin.

2.) Find the first-quadrant point of the curve xy=24 that is closest to the point (1,4)

3.) Find teh points on teh sphere with center (1,2,3) and radius 6 that are closest to and farthest from the origin
• Oct 16th 2009, 09:11 PM
mr fantastic
Quote:

Originally Posted by messianic
Can someone help me on the following Lagrange multiplier problems:

1.) Find the points of the parabola y = (x-1)^2 that are closest to the origin.

2.) Find the first-quadrant point of the curve xy=24 that is closest to the point (1,4)

3.) Find teh points on teh sphere with center (1,2,3) and radius 6 that are closest to and farthest from the origin

1. Find the point that minimises \$\displaystyle D = x^2 + y^2\$ subject to the constraint \$\displaystyle y = (x - 1)^2\$.

2. Find the point that minimises \$\displaystyle D = (x-1)^2 + (y-4)^2\$ subject to the constraint \$\displaystyle xy = 24\$.

3. Find the points that minimise and maximise \$\displaystyle D = x^2 + y^2 + z^2\$ subject to the constraint \$\displaystyle (x-1)^2 + (y-2)^2 + (z-3)^2 = 6^2\$.

If you need more help please post all your working and state where you get stuck.