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.


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: