# Tag Info

## New answers tagged lagrange-multiplier

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Note: It is more convenient for the calculations to assume (without loss of generality) that $c=1$. The Hessian matrix of $f$ is equal to $$\left(\frac{d^2f(x)}{dx_idx_j}\right)_{i,j=1,\ldots n}=\mathbb{0}_{n\times n}$$ and thus positive semidefinite (the zero matrix). For example ...

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f(x,y) = x + 2y^2 - 3(4x^2 + y^2) = -12x^2 + x - y^2. The function g(x) = -12x^2 + x is a parabola with vertex x = -b/2a = -1/(2(-12)) = 1/24. So max g = g(1/24) = 1/48 ==> max f = 1/48 at (x,y,z) = (1/24,0,1/144).

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