1. Let C, denote the circle r +N=1 and consider the function F(, y) = r'(y- 1. (a) Suppose points are constrained to lie on C. Find the coordinates of all the constrained stationary points of Fand...

Extracted text: 1. Let C, denote the circle r +N=1 and consider the function F(, y) = r'(y- 1. (a) Suppose points are constrained to lie on C. Find the coordinates of all the constrained stationary points of Fand identify which, if any, are constrained maxima or minima. (b) Consider the region D that lies within C, and also satisfies y 20. Find the maximum and minimum of Fover the region D (including its boundaries), and give the coordinates at which these values occur. (c) Now let C, denote the circle + y for some ye R, and suppose points are constrained to le on C, Let (a, y) denote the coordinates of the maximum value of Fsubject to this constraint. By calcutating these coordinates when y is large, ahow that the ratio of a" and y" approaches a constant value a (independent of ) as