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Bah calculus calculus & more calculus

  1. May 13, 2010 #1
    got a simple problem.
    the question is find min value for f=x*y+(z^2) with constraints 2*x -y=8, and co-ordinates where it occurs.
    so far what i did.


    i got λ=-2

    is this right? and is that the only λ value?

    how do i even start to find equilibrium solutions & general solution to ((t/2)-2)*sin(y), we weren't taught or shown how to find it involving sin,cos, tan?
    for general solution i should take it as separable to find the general solution? but how do i start? sin, cos, tan bah
    Last edited: May 13, 2010
  2. jcsd
  3. May 13, 2010 #2


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    Homework Helper

    you could probaby substitute directly into that function & minimise
  4. May 13, 2010 #3


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    otherwise lagrange multipliers are alway good...
  5. May 13, 2010 #4


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    I think you are trying to use "Lagrange multipliers" as lanedance suggested but you seem to have no idea how to do that.

    You write, correctly, that [itex]\nabla f= \lambda \nabla g[/itex] but then "F(x,y,z)=f(x,y)-λg(x,y,z)" and "F=(xy+z^2)-λ(2x-y-8)" which have nothing to do with what you wrote previously.

    [itex]\nabla f[/itex] is the vector [itex]y\vec{i}+ x\vec{j}+ 2z\vec{k}[/itex] and [itex]\nabla g= 2\vec{i}- \vec{j}[/itex].

    "[itex]\nabla f= \lambda \nabla g[/itex]" is now
    [itex]y\vec{i}+ x\vec{j}+ 2z\vec{k}= \lambda 2\vec{i}- \vec{j}[/itex]

    Looking at the individual components of that, [itex]y= 2\lambda[/itex], [itex]x= -\lambda[/itex], and [itex]z= 0[/itex].

    Now, you have [itex]y= 2\lambda[/itex] but you have [itex]x= \lambda[\itex] rather than [itex]x= -\lambda[/itex]. Perhaps that is just a typo. In any case, they do not give "[itex]\lambda= -2[/itex] because you have no reason to believe x= -2 or y= -4!.

    Rather, [itex]x= -\lambda[/itex] says that [itex]\lambda= -x[/itex] and so [itex]y= 2\lambda= -2x[/itex]. Putting that into the constraint 2x- y= 8 gives 2x+ 2x= 4x= 8 so x= 2 and y= -4. The solution is (2, -4, 0).

    Is this a completely different problem? Then what is the problem? I associate "equilibrium solutions & general solution" with differential equations but you give no differential equation. Are you talking about dy/dt= ((t/2)- 2)sin(y) or some other problem? Please state the entire problem.

    And a general suggestion: if you want people who are really good at math to help you (hopefully more politely than I did), stop dissing mathematics!
  6. May 19, 2010 #5

    i didn't diss maths. why would i diss maths if im majoring in maths? its called sense of humour. last time im using this forum, its like dictatorship here no freedom.
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