Is the maximum inside or on the boundary? So let's discuss why the distance between (2, 0) and (1, 1) is less than or equal to 1.If we say that x minus 2 squared plus y squared equals 1, then the distance from (2,0) to (1, 1) is equal to 1. In other words, the region bounded by a circle centered at(2, 0) and with radius 1 includes the circle itself and everything inside of it. We will now consider the problem of finding the maximum of a function on a region.As we did in warm-up, we first take a picture of the gradient of the function and try todetermine where the function has its largest value. The boundary of the region R is a circle with a center at the origin. The region Rincludes the boundary and is inside the circle. The picture shows a graph of thefunction f, where f(x) denotes the value of the function at point x on its domain. Wewill determine where f is largest.
What is the maximum value of this function on the inside of the region R, or is it onthe boundary of R?