1.) Find and classify the critical points of each function. (a.) f(x,y)=x^2 ? xy
ID: 1948657 • Letter: 1
Question
1.) Find and classify the critical points of each function.(a.) f(x,y)=x^2 ? xy + y^2 + 9x ? 6y +10
(b.) f(x,y)=2x^3 + xy^2 + 5x^2 + y^2
(c.) f(x,y)=3xy ? x^(2)y ? xy^2
(d.) f(x,y)=x^4 + y^4 ? 4xy + 2
(e.) f(x,y)=x^(2)y + xy^2 + x + y + 1
Explanation / Answer
a max of 17 at ( 2 , 3 ) , min of 0 at (0,0)... b or where df/dy = 0 and d2f/dy2 < 0 find the highest f that meets those criteria (if one exists for a finite value) minimum is where df/dx = 0 and d2f/dx2 > 0 or where df/dy = 0 and d2f/dy2 > 0 find the lowest f that meets those criteria (if one exists for a finite value) saddle point is where df/dx = 0 and df/dy = 0 and the signs of d2f/dx2 and d2f/dy2 are opposite (i.e. one positive one negative) c ( 0, 0 ) : F?? = 0, F?? = 0 , F?? = 3, det(H) = -9 Since det(H)0 and F??Related Questions
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