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I have a function:

$$f(x, \lambda) = x_1^2 + x_2^2 + x_3^2 + \lambda(1-x_1 - x_2 - x_3)$$

If I take the first derivative test, what should I interprete from the results about the critical points $f(x*, \lambda*)$?

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    critical points are at 0? – 2017-01-27
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    Hi Markoff, thanks for the answer. my question was incomplete actually. now I have edited it. please check – 2017-01-27
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    do you want to find maximum value of $x^2_1+x^2_2+x^2_3$ subject to the constraint $x_1+x_2+x_3=1$? – 2017-01-27
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    I am trying to get a critical point by taking the first derivative. I am given the condition $x_1 +x_2+x_3 = 1$, but that can be used after taking the derivative test. My prob is when I take the partial derivative, I get $1-x_1 -x_2-x_3$ for $d f/d \lambda$. How can I solve for the solution using the condition? – 2017-01-27
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    $2x_1=\lambda, 2x_2=\lambda, 2x_3=\lambda$ >> $x_1=x_2=x_3=1/3$ – 2017-01-27
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    I got that already. How to find the actual solution from there?! – 2017-01-27
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    So critical point is at $x_1=x_2=x_3=1/3$. Does it answer your question or I am missing something? – 2017-01-27

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