a)$ f(x_1,x_2,x_3) = x^3_1+x^3_2+x^3_3 \rightarrow extr$ subject to the constraint (sphere) $x^2_1+x^2_2+x^2_3 =4$ (problem with $n=3$ and $m=1$)\\
a)$ f(x_1,x_2,x_3) = x^3_1+x^3_2+x^3_3 \rightarrow extr$ subject to the constraint (sphere) $x^2_1+x^2_2+x^2_3 =4$ (problem with $n=3$ and $m=1$)\\
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 40E
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What is/are the extremizers candidates (the critical points)by using the Lagrange multiplier method, for each one of the following problems:\\
a)$ f(x_1,x_2,x_3) = x^3_1+x^3_2+x^3_3 \rightarrow extr$ subject to the constraint (sphere) $x^2_1+x^2_2+x^2_3 =4$ (problem with $n=3$ and $m=1$)\\
b) $f\rightarrow extr$ with $f$ the same function as in (a), but now not for all points of the sphere $x^2_1+x^2_2+x^2_3 =4$ only for those such points of the sphere that also belong to the plane $x_1+x_2+x_3 =1$ (problem with $n=3$ and $m=2$)?
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