Question

Use Lagrange multipliers to find the point(s) on the sphere

x²+y²+z²=1
that are at the greatest distance from the point (0,1,2).

Answer 1

To find the point(s) on the sphere x²+y²+z²=1 that are at the greatest distance from the point (0,1,2) using Lagrange multipliers, we need to define an objective function and a constraint function. By setting up the Lagrangian equation and finding the partial derivatives, we can solve for the coordinates of the point(s) on the sphere that are farthest away from the given point.

Step-by-step explanation:

To find the point(s) on the sphere x²+y²+z²=1 that are at the greatest distance from the point (0,1,2) using Lagrange multipliers, we need to define an objective function and a constraint function. Let the objective function be the distance between the given point and a point on the sphere, and the constraint function be the equation of the sphere. By setting up the Lagrangian equation and finding the partial derivatives, we can solve for the coordinates of the point(s) on the sphere that are farthest away from the given point.