Find values of x and y such that both f,(x,y)= 0 and fy (x.y)=D0. f(x.y) =x + xy +y² - 3x+2

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A: This question is related to partial derivatives.

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Q: Prove that if x+y=%30 then y=-x

A: See the attachment

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Q: Let f(x, y) = x²-2 y.(y+4)

A: We can compute the determinant.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.