Example

Example: Location of a Local Minimum, Maximum or Saddle Point

A flat plate is heated such that the temperature, T at any point (x, y) can be described as T = x² + 2y² – x. Find the temperature at the coldest point on the plate.

   Solution

Take the partial derivatives and set them equal to zero:

  
       
   

            x = 1/2

     

        y = 0

Now plug these values back into the equation for temperature:

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