TITLE: Find the equation of the tangent plane to the graph of the function given by $f (x, y) = x^2 − 2xy + 2y^2$ having slope 2 to +x and slope 4 to +y
QUESTION [2 upvotes]: Find the equation of the tangent plane to the graph of the function given by $f (x, y) = x^2 − 2xy + 2y^2$ having slope 2 in the positive x-direction and slope 4 in the positive y-direction.
It seems easy but i'm having trouble finding where to start

REPLY [0 votes]: Isn't it just this $z= f(a,b) + (x-a)(f_x(x,y)+(y-b)(f_b(y-b)$
i find a and b by solving 2x-2y=2 and 4y-2x = 4.
We gets you x=4 and y-3 and f(4,3) = 18
so z the tangent now is....
Z = 18 + (x-4,y-3)(2,4) = 2x=4y-2
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