Lecture Note
University
Massachusetts Institute of TechnologyCourse
Multivariable CalculusPages
2
Academic year
2022
Sporkz
Views
76
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?
Is the Maximum Inside or on the Boundary?
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