(1)
![(2a+b^2)_{min}=?\\ f(a)=2a+(9-a)^2=2a+81-18a+a^2=a^2-16a+81\\ f'(a)=(a^2-16a+81)'=2a-16\\\\ f'(a)=0\\ 2a-16=0\\ 2a=16\\ a=8\\ b=9-a=9-8=1\\ ----------------------------\\\\ f'(a)\\ -------[8]++++++\ \textgreater \ a\\\\ ----------------------------\\\\ f_{min}=f(8)](https://tex.z-dn.net/?f=%282a%2Bb%5E2%29_%7Bmin%7D%3D%3F%5C%5C%0Af%28a%29%3D2a%2B%289-a%29%5E2%3D2a%2B81-18a%2Ba%5E2%3Da%5E2-16a%2B81%5C%5C%0Af%27%28a%29%3D%28a%5E2-16a%2B81%29%27%3D2a-16%5C%5C%5C%5C%0Af%27%28a%29%3D0%5C%5C%0A2a-16%3D0%5C%5C%0A2a%3D16%5C%5C%0Aa%3D8%5C%5C%0Ab%3D9-a%3D9-8%3D1%5C%5C%0A----------------------------%5C%5C%5C%5C%0Af%27%28a%29%5C%5C%0A-------%5B8%5D%2B%2B%2B%2B%2B%2B%5C+%5Ctextgreater+%5C+a%5C%5C%5C%5C%0A----------------------------%5C%5C%5C%5C%0Af_%7Bmin%7D%3Df%288%29)
Ответ:
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(2)
![P=2*(a+b)=12\\ a+b=6\\ b=6-a\\ ---------------------------\\\\ S(a)=a*b=a*(6-a)=6a-a^2\\ S_{max}=? S'(a)=(6a-a^2)'=6-2a\\\\ S'(a)=0\\ 6-2a=0\\ 2a=6\\ a=3\\\\ ----------------------------\\\\ S'(a)\\ ++++++[3]------\ \textgreater \ a\\\\ S_{max}=S(3)\\ a=3\\ b=6-3=3](https://tex.z-dn.net/?f=P%3D2%2A%28a%2Bb%29%3D12%5C%5C%0Aa%2Bb%3D6%5C%5C%0Ab%3D6-a%5C%5C%0A---------------------------%5C%5C%5C%5C%0AS%28a%29%3Da%2Ab%3Da%2A%286-a%29%3D6a-a%5E2%5C%5C%0AS_%7Bmax%7D%3D%3F%0AS%27%28a%29%3D%286a-a%5E2%29%27%3D6-2a%5C%5C%5C%5C%0AS%27%28a%29%3D0%5C%5C%0A6-2a%3D0%5C%5C%0A2a%3D6%5C%5C%0Aa%3D3%5C%5C%5C%5C%0A----------------------------%5C%5C%5C%5C%0AS%27%28a%29%5C%5C%0A%2B%2B%2B%2B%2B%2B%5B3%5D------%5C+%5Ctextgreater+%5C+a%5C%5C%5C%5C%0AS_%7Bmax%7D%3DS%283%29%5C%5C%0Aa%3D3%5C%5C%0Ab%3D6-3%3D3)
Прямоугольная клумба должна быть квадратной, что бы её площадь была максимальной! со стороной
Ответ:
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(2)
Прямоугольная клумба должна быть квадратной, что бы её площадь была максимальной! со стороной