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$g(a,b,c)=3a-2b+c$, B is a closed unit ball in $\mathbb R^3$. Find the max/min of g on B. What is the behavior of $g$ on the open unit ball, and the boundary of the unit ball?

I think the unit ball can be defined by the equation $x^2+y^2+z^2=1$. Should I minimize $g$ on this surface? how do I discuss the behavior of $g$ on the open ball, and the boundary?

hobbitty
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    By Lagrange multipliers (or intuition), the max/min will be at one of the two points where the line $t(3,-2,1), t\in \mathbb R$ intersects the unit sphere. – William Stagner Apr 02 '15 at 05:52
  • @WilliamStagner Thank you. I am still unsure what the question is looking for when it asks about behavior on $B^O$ and boundary of B. Any clues? – hobbitty Apr 02 '15 at 06:04
  • FWIW, the closed unit ball is $x^2 + y^2 + z^2 \le 1$, the open unit ball is $x^2 + y^2 + z^2 \lt 1$. – PM 2Ring Apr 02 '15 at 06:10

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