1)15÷3×2=10 (м)-вторая часть верёвки.
2)15+10+17=42 (м)
Ответ:42 метра длина верёвки.
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![f= \frac{3+2x}{x-5} \\ f'=( \frac{3+2x}{x-5} )'= \frac{(3+2x)'(x-5)-(3+2x)(x-5)'}{(x-5)^2}= \frac{2(x-5)-(3+2x)}{(x-5)^2}= \\ = \frac{2x-10-3-2x}{(x-5)^2}=\frac{-13}{(x-5)^2} \\ ](https://tex.z-dn.net/?f=f%3D+%5Cfrac%7B3%2B2x%7D%7Bx-5%7D+%5C%5C%0Af%27%3D%28+%5Cfrac%7B3%2B2x%7D%7Bx-5%7D+%29%27%3D+%5Cfrac%7B%283%2B2x%29%27%28x-5%29-%283%2B2x%29%28x-5%29%27%7D%7B%28x-5%29%5E2%7D%3D+%5Cfrac%7B2%28x-5%29-%283%2B2x%29%7D%7B%28x-5%29%5E2%7D%3D+%5C%5C%0A%3D+%5Cfrac%7B2x-10-3-2x%7D%7B%28x-5%29%5E2%7D%3D%5Cfrac%7B-13%7D%7B%28x-5%29%5E2%7D+%5C%5C%0A%0A)
Ответ: А
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![f(x)=x^3-6x^2+5\\ f'(x)=3x^2-12x\\ 3x^2-12x=0\\ 3x(x-4)=0\\ x_1=0\\ x_2=4](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3-6x%5E2%2B5%5C%5C%0Af%27%28x%29%3D3x%5E2-12x%5C%5C%0A3x%5E2-12x%3D0%5C%5C%0A3x%28x-4%29%3D0%5C%5C%0Ax_1%3D0%5C%5C%0Ax_2%3D4)
![f'(x)\ \textless \ 0](https://tex.z-dn.net/?f=f%27%28x%29%5C+%5Ctextless+%5C+0)
при
![x \in (0;4)](https://tex.z-dn.net/?f=x+%5Cin+%280%3B4%29)
![f'(x)\ \textgreater \ 0](https://tex.z-dn.net/?f=f%27%28x%29%5C+%5Ctextgreater+%5C+0+)
при
![x\in (-\infty;0)\cup(4;+\infty)](https://tex.z-dn.net/?f=x%5Cin+%28-%5Cinfty%3B0%29%5Ccup%284%3B%2B%5Cinfty%29)
Производная меняет свой знак с "+" на "-" в точке х = 0, поэтому эта точка - максимум, в точке х = 4 - с "-" на "+" - в этой точке минимум
Ответ: Г
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![f(x)=x^5+x^4\\ f'(x)=5x^4+4x^3\\ f''(x)=20x^3+12x^2\\ f'''(x)=60x^2+24x\\](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E5%2Bx%5E4%5C%5C%0Af%27%28x%29%3D5x%5E4%2B4x%5E3%5C%5C%0Af%27%27%28x%29%3D20x%5E3%2B12x%5E2%5C%5C%0Af%27%27%27%28x%29%3D60x%5E2%2B24x%5C%5C)
Ответ: В
45 км 530 м
+37 км 470 м
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83 км 000 м
метры составляя 1000 дают 1 км.