Solve please ?

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1 Answer
Oct 18, 2017

2

Explanation:

Given f(x,y) = x^2+4x y+6y^2-4y+4

The local stationary points are the solutions for

grad f(x,y) = (f_x,f_y) = (2x+4y,4x+12y-4) = (0,0)

then the stationary point's set is (x,y) =(-2,1)

The stationary point's qualification is given analyzing the eigenvalues for grad^2f = H so

H = 2((1,2),(2,6)) with characteristic polynomial

p(lambda)=8 - 14 lambda + lambda^2 and with roots

lambda = 7 pm sqrt41 both positive, then the stationary point at (-2,1) is a local minimum point. It is also a global minimum point and f(-2,1) = 2