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1. Section 12.8, Page 912, question 54.
0 f(x,2x) are Minima Absolute
f(2,0)at 16 is Maximum Absolute
0)1)(( 16)1)2(()1())1(2()(),(
20 ,1 line On the
0)4)1(4(16)4)2(4()44())42(2()(),(
21 ,42 line On the
0)11(1)10()1())1(2()(),(
10 ,1 line On the
0))2(2()2,(
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042),(048),(
42)2(2),(482)2(2),(
)2(),(
2
5
2
2
5
2
2
5
2
2
5
2
2
1
2
1
2222
2222
2
2
=
=−==−=−=+−−==
≤≤+−=
=−==−=−=+−−==
≤≤+−=
=−==−=−=+−==
≤≤+=
=−=
==−=−
=−==−=
−=−−=−=−=
−=
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2. Section 12.9, Page 918, question 22.
32 32
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y. real allfor defined is
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3
2
3
2
3
2
3
2
6
4812
6
)3)(8(414412
2222
84
4284
84
42
22
222222
2
2
2
−=∴−
>−−−−−−<
+−
+−±=
===+−+−=+−−=+−=
=+=
+−+=+−++=
=−+−+−+−−+−+−=
∂
∂
∂
∂
±
−±
∂
∂
+−
−++−
+−
−
∂
∂
yy
ject
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y
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3. Section 12.10, Page 928, question 40.
150500100)0,25,0(
25500:50
00:0
00:21:20
02222:122
22
),,(0),,(
222),,(50),,(
22),,(100),,(
2
2
222
222
22
=++=
=====++
====−
====−=
=+=+===
+=
−=∇=−=
++=∇=++=
+=∇++=
T
yzxSincezyx
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