Use Lagrange multipliers to minimize the function subject to the following constraint: ​ ​ Assume that x and y are positive. ​

Use Lagrange multipliers to minimize the function subject to the following two constraints. Assume that x, y, and z are nonnegative. 

The temperature at the point on a metal plate is modeled by , . Find the directions of no change in heat on the plate from the point .  

Let , where , , and . Find . ​

Find the maximum value of the directional derivative at the point of the function . Round your answer to two decimal places.  

Find for function .  

Which of the following would be a complication of a severe burn?

Find the minimum distance from the point to the plane .

Suppose the centripetal acceleration of a particle moving in a circle is , where v is the velocity and r is the radius of the circle. Approximate the maximum percent error in measuring the acceleration due to errors of 7% in v and 5% in r. ​

Let , where and . Find . ​