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Question Number 144753 by mondlihk last updated on 28/Jun/21

Answered by ajfour last updated on 28/Jun/21

(∂f/∂x)=3x^2 −3ay=0 ⇒ y=(x^2 /a) similarly (∂f/∂y)=3y^2 −3ax=0 ⇒ y^2 =ax so (x^4 /a^2 )=ax x=a f=2a^3 −3a^3 =−a^3 (∂^2 f/∂x^2 )=(∂^2 f/∂y^2 )= 6a >0 hemce local minima at x=y=a where f(x,y)=−a^3

∂f∂x=3x2−3ay=0⇒y=x2asimilarly∂f∂y=3y2−3ax=0⇒y2=axsox4a2=axx=af=2a3−3a3=−a3∂2f∂x2=∂2f∂y2=6a>0hemcelocalminimaatx=y=awheref(x,y)=−a3

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