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Bess [88]
3 years ago
10

PLEASE HELP 15 POINTS -8 - h = 2(-.5h + 4)

Mathematics
1 answer:
Vanyuwa [196]3 years ago
3 0

Answer:

h= -6

Step-by-step explanation:

-8-h=2(-.5h+4)

-8-h=h+4

-2h=12

h=-6

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
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First find the critical points of <em>f</em> :

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f(1,0)=-7

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t

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\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0

\implies\sin t=0\text{ OR }1+5\cos t=0

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t=\pi\implies f(-10,0)=235

t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299

So <em>f</em> has a minimum of -7 and a maximum of 299.

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