X^2+Y^2=36求(X+y)^2+y^2的最大值,不能求导
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X^2+Y^2=36求(X+y)^2+y^2的最大值,不能求导
X^2+Y^2=36求(X+y)^2+y^2的最大值,不能求导
X^2+Y^2=36求(X+y)^2+y^2的最大值,不能求导
依圆的参数方程,设x=6cosθ,y=6sinθ,则
(x+y)²+y²
=x²+2y²+2xy
=36cos²θ+72sin²θ+72sinθcosθ
=36(sin²θ+cos²θ)+36sin²θ+72sinθcosθ
=36+36(1-cos2θ)/2+36sin2θ
=54+36(sin2θ-cos2θ)
=54+36√2sin(2θ-π/4).
sin(2θ-π/4)=1时,((x+y)²+y²)|max=54+36√2;
sin(2θ-π/4)=-1时,((x+y)²+y²)|min=54-36√2.
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