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melisa1 [442]
2 years ago
14

I got 4.9 and 40 i dont know if im right

Mathematics
1 answer:
Nata [24]2 years ago
4 0

Answer:

I got 40 aswell

Step-by-step explanation:

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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex
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f(x_1,\ldots,x_n)=x_1+\cdots+x_n=\displaystyle\sum_{i=1}^nx_i

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L(x_1,\ldots,x_n,\lambda)=\displaystyle\sum_{i=1}^nx_i+\lambda\left(\sum_{i=1}^n{x_i}^2-4\right)

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L_{x_i}=1+2\lambda x_i=0\implies x_i=-\dfrac1{2\lambda}

for 1\le i\le n, and

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or

x_i=-\dfrac1{2\left(-\frac{\sqrt n}4\right)}=\dfrac2{\sqrt n}

At these points we get a value of f(x_1,\cdots,x_n)=\pm2\sqrt n, i.e. a maximum value of 2\sqrt n and a minimum value of -2\sqrt n.

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Step-by-step explanation:

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