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|00000030| 67 68 74 7b 43 68 61 70 | 74 65 72 20 33 3a 20 41 |ght{Chap|ter 3: A|
|00000040| 6e 73 77 65 72 73 20 31 | 7d 0a 5c 62 65 67 69 6e |nswers 1|}.\begin|
|00000050| 7b 64 6f 63 75 6d 65 6e | 74 7d 0a 0a 5c 42 66 7b |{documen|t}..\Bf{|
|00000060| 43 68 61 70 74 65 72 20 | 33 3a 20 41 6e 73 77 65 |Chapter |3: Answe|
|00000070| 72 73 20 31 20 5c 68 66 | 69 6c 6c 20 4a 61 63 6b |rs 1 \hf|ill Jack|
|00000080| 20 4b 2e 20 43 6f 68 65 | 6e 20 5c 68 66 69 6c 6c | K. Cohe|n \hfill|
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|000000c0| 74 65 6d 20 54 68 65 20 | 73 6c 6f 70 65 20 6f 66 |tem The |slope of|
|000000d0| 20 24 66 28 78 29 24 20 | 61 74 20 24 78 20 3d 20 | $f(x)$ |at $x = |
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|00000200| 63 29 24 20 61 6e 64 20 | 70 6f 73 69 74 69 76 65 |c)$ and |positive|
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|000002b0| 6f 6e 20 24 28 63 2c 20 | 62 5d 24 20 61 6e 64 20 |on $(c, |b]$ and |
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|00000320| 20 64 65 72 69 76 61 74 | 69 76 65 20 6f 66 20 24 | derivat|ive of $|
|00000330| 66 28 78 29 20 3d 20 78 | 5e 33 20 2d 20 32 78 20 |f(x) = x|^3 - 2x |
|00000340| 2b 20 31 24 20 69 73 20 | 24 66 27 28 78 29 20 3d |+ 1$ is |$f'(x) =|
|00000350| 20 33 78 5e 32 20 2d 20 | 32 20 3d 20 33 28 78 5e | 3x^2 - |2 = 3(x^|
|00000360| 32 20 2d 20 32 2f 33 29 | 20 3d 20 32 20 28 78 20 |2 - 2/3)| = 2 (x |
|00000370| 2d 20 5c 73 71 72 74 7b | 20 32 2f 33 7d 29 28 78 |- \sqrt{| 2/3})(x|
|00000380| 20 2b 20 5c 73 71 72 74 | 7b 32 2f 33 7d 29 24 2e | + \sqrt|{2/3})$.|
|00000390| 20 20 20 54 68 75 73 20 | 6f 6e 20 74 68 65 20 63 |   Thus |on the c|
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|000003b0| 5b 2d 31 2c 20 31 5d 24 | 2c 20 77 65 20 68 61 76 |[-1, 1]$|, we hav|
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|000003e0| 20 26 20 24 20 5b 2d 31 | 2c 20 2d 5c 73 71 72 74 | & $ [-1|, -\sqrt|
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|00000440| 26 20 24 2b 24 20 26 20 | 24 2d 24 20 5c 5c 20 20 |& $+$ & |$-$ \\  |
|00000450| 5c 68 6c 69 6e 65 0a 24 | 66 24 20 26 20 24 5c 73 |\hline.$|f$ & $\s|
|00000460| 65 61 72 72 6f 77 24 20 | 26 20 24 5c 6e 65 61 72 |earrow$ |& $\near|
|00000470| 72 6f 77 24 20 26 20 24 | 5c 73 65 61 72 72 6f 77 |row$ & $|\searrow|
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|00000490| 0a 54 68 65 20 61 72 72 | 6f 77 73 20 69 6e 20 74 |.The arr|ows in t|
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|00000530| 20 61 72 65 20 24 78 20 | 3d 20 2d 31 24 20 61 6e | are $x |= -1$ an|
|00000540| 64 20 24 78 20 3d 20 5c | 73 71 72 74 7b 32 2f 33 |d $x = \|sqrt{2/3|
|00000550| 7d 24 2c 20 65 76 61 6c | 75 61 74 69 6e 67 20 24 |}$, eval|uating $|
|00000560| 66 24 20 61 74 20 74 68 | 65 73 65 20 70 6f 69 6e |f$ at th|ese poin|
|00000570| 74 73 20 73 68 6f 77 73 | 20 74 68 61 74 20 74 68 |ts shows| that th|
|00000580| 65 20 6d 61 78 69 6d 75 | 6d 20 69 73 20 61 74 20 |e maximu|m is at |
|00000590| 24 78 20 3d 20 5c 73 71 | 72 74 7b 32 2f 33 7d 24 |$x = \sq|rt{2/3}$|
|000005a0| 2e 20 20 53 69 6d 69 6c | 61 72 6c 79 20 24 78 20 |.  Simil|arly $x |
|000005b0| 3d 20 2d 5c 73 71 72 74 | 7b 32 2f 33 7d 24 20 67 |= -\sqrt|{2/3}$ g|
|000005c0| 69 76 65 73 20 74 68 65 | 20 6d 69 6e 69 6d 75 6d |ives the| minimum|
|000005d0| 2e 20 20 53 65 65 20 46 | 69 67 75 72 65 20 33 2e |.  See F|igure 3.|
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