Neil has a small, but valuable, art collection. He would like to help his son, Kamal, start his own collection. He writes a letter to Kamal on his twenty-first birthday: “Kamal, I would like to help you start your own private art collection. I am thinking of giving you the small Picasso print that you have always loved. The next time you visit we can talk about whether that print is the right piece to start your collection.” A few months later, Neil dies. The Picasso print is still hanging in the study. Neil’s other children argue that the print should be included in Neil’s estate, which is to be divided equally among his children. Kamal argues that his father already gave him the print. Which of the following is true?

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. ​