For each of the following functions, find the maximum and minimum values of the function on the circular disk: x^2+y^2≤1. do this by looking at the level curves and gradients. f(x, y)=x+y+4 maximum value =

The gradient of the level curve f(x,y) can be found using partial derivatives.



This means that the max value lies on the vector <1,1> which is equivalent to the line y = x.

Find the points along edge of disc where y = x.



These 2 solutions provide both max and min values.

Let x be positive will give max value for f(x,y)