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 to determine where the function has its largest value. [Graph] The boundary of the region R is a circle with a center at the origin. The region R includes the boundary and is inside the circle. The picture shows a graph of the function f. where f(x) denotes the value of the function at point x on its domain. We will determine where f is largest. What is the maximum value of this function on the inside of the region R, or is it on the boundary of R?
