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Klio2033 [76]
3 years ago
10

Solve the following 16,17,18,19,20.​

Mathematics
1 answer:
Shtirlitz [24]3 years ago
6 0

Answer:

show your work

Step-by-step explanation:

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The Lagrangian is

L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)

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L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}

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Substitute x,y into the last equation and solve for \lambda:

\left(-\dfrac1{2\lambda}\right)^2+\left(-\dfrac2\lambda\right)^2=9\implies\lambda=\pm\dfrac{\sqrt{17}}6

Then we get two critical points,

(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)

We get an absolute maximum of 3\sqrt{17}\approx12.369 at the second point, and an absolute minimum of -3\sqrt{17}\approx-12.369 at the first point.

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