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Question: Consider the function ay) = (4 - 1'2 - 92%\"- (1) Find the maximal and minimal values of function ay! under the constraint on + y2 = 1. Hint: Under the constraint 3:2 + y2 = 1, we have 3; = a 1 - 3:2, 1 5 :1: 5 1. and therefore f(1=,y)= 9(1') = 391\"\" 1'12 with 1 s :r: s 1. It sufces to nd maximal and minimal values of 9(3) on the closed interval :1: E [-1, 1]. 0n the closed interval :1: e [1.1], one needs to compare the function values at all the stationary points of 9(3) on [1, 1] and the endpoints z : 11. (2) Find the maximal and minimal values of function ay) under the constraint 1532+y253 Hint: 1 g 1:2 + 3,12 S 3 represents an annular region between the two circles 2 $2+yz=1 and 1: +y2=3. Step 1: Find all stationary points of x, 3;) satisfying 1 5 1:2 + y2 s 3 (inside the annular region). Step 2: Find the maximal and minimal values on the two circles, i.e., under constraint 3:2 + y2 = 1 and under constraint 1'2 + y2 = 3, respectively, by using the method in part (1). Step 3: Compare the function values of x, 3;) at the points obtained in Step 1 and Step 2 to nd the maximal and minimal values