HW Extra $1$: Problem $6$

$(10$ points$)$

Find the minimum and maximum values of the function $f(x,y,z)=3x+2y+4z$ subject to the constraint $x^2+2y^2+6z^2=1.$

$f_{\text{m}\text{a}\text{x}}=$

$f_{\text{m}\text{i}\text{n}}=$

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