Is the set X={(x_{1},x_{2})|x_{2}^{2}>=4x_{1}} convex or not ? How to prove it mathematically ?

This is a problem in Linear Programming Problem (LPP). Please help

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- Feb 3rd 2013, 08:57 PMSuvadipConvex set in LPP
Is the set X={(x

_{1},x_{2})|x_{2}^{2}>=4x_{1}} convex or not ? How to prove it mathematically ?

This is a problem in Linear Programming Problem (LPP). Please help - Feb 3rd 2013, 11:54 PMchiroRe: Convex set in LPP
Hey Suvadip.

Is it possible to use the Hessian for this system? - Feb 11th 2013, 05:57 PMHallsofIvyRe: Convex set in LPP
It seems to me the simplest way is just to graph it. Using x= x1, y= x2, the graph of y^2= 4x is a parabola and the set {(x, y)| y^2>= x} is the set of points

**outside**the parabola. That would lead me to look at the points (1, 2) and (1, -2). 2^2= 4> 1 and (-2)^2> 1 so both (1, 2) and (1, -2) is in the set. But (1, 0) is NOT.