Probem22+Sam+B,+Yutong

This does work out beautifully but it really is a situation where you might be better off writing this out on paper and scanning it in! I agree with your work so far, just what is dy/dx? I would recommend Yutong's approach...you are maximizing A = xy, where y = b√ (1-x²/a²). (show why -- yutong, you are on the right track but simplify what you have). You will need ot take the derivative of A, which will of course require you to use the product rule!

problem 22 A= x*y where 0<X<2a, 0<Y<2b f(x) = X^2/a^2 +Y^2/b^2= 1 f(x)=x^2b^2+y^2a^2=a^2b^2 isolate x and we get x= squreroot((a^2*b^2-y^2*a^2)/b^2) substitute squreroot((a^2*b^2-y^2*a^2)/b^2) for x in A= x*y we get A = y * squreroot((a^2*b^2-y^2*a^2)/b^2) take the derivative of A and we have d(A) = squreroot((a^2*b^2-y^2*a^2)/b^2)+y*( 2y/squreroot((a^2*b^2-y^2*a^2)/b^2)*2) ugh... .....-_-..... solve from there and find the value of y where d(a) = 0?

Sam's attempt: