Find the greatest and the small value of f(x,y) = xy on the ellipse x^2 + y^2 = 1
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(x/2√2 - y/√2)×(x/2√2 - y/√2) >= 0
x×x/8 +y×y/2 >= x×y/2
On the ellipse,
2 >= x×y
The equality holds when the line x/2√2=y/√2 intersects the ellipse i.e. (2,1) and -(2,1). Max value of x×y is 2 and min value is -2 because if (x,y) lies on ellipse then so is (-x,y).
write or wrong
x×x/8 +y×y/2 >= x×y/2
On the ellipse,
2 >= x×y
The equality holds when the line x/2√2=y/√2 intersects the ellipse i.e. (2,1) and -(2,1). Max value of x×y is 2 and min value is -2 because if (x,y) lies on ellipse then so is (-x,y).
write or wrong
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