roblem 8. (11.8/46) a) Find the extrema of > x,y, subject to the constraints Ex," =1 and Ey? =1. [Hint: This is a problem in R2" . The Method of Lagrange Multipliers w/multiple constraints generalizes. ] a; b b) Put x = and y, = to show that Cab, s Ja, Cb,? for any numbers VEa, VEb , a1,... d,,b,,...b, . This inequality is known as the Cauchy-Schwarz Inequality. [Note: In vector notation, if we write a = (a,...,d, ) and b = (b,...,b, ) and if we use Lagrange Multipliers to determine both the maximum and minimum values, this says that a . b