Найдите наибольшее и наименьше значения заданной функции на заданном отрезке
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˚_˚ǁ help please(
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Ответы
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![y=x^2-8x+19 \\ y'=2x-8 \\ 2x-8=0 \\ x=4 \\ y(-1)=(-1)^2-8*(-1)+19=1+8+19=28 \\ y(4)=4^2-8*4+19=16-32+19=3 \\ y(5)=5^2-8*5+19=25-40+19=4 \\ y_{min} =y(4)=3; y_{max}=y(-1)=28 y=x^2-8x+19 \\ y'=2x-8 \\ 2x-8=0 \\ x=4 \\ y(-1)=(-1)^2-8*(-1)+19=1+8+19=28 \\ y(4)=4^2-8*4+19=16-32+19=3 \\ y(5)=5^2-8*5+19=25-40+19=4 \\ y_{min} =y(4)=3; y_{max}=y(-1)=28](https://tex.z-dn.net/?f=y%3Dx%5E2-8x%2B19+%5C%5C+y%27%3D2x-8+%5C%5C+2x-8%3D0+%5C%5C+x%3D4+%5C%5C+y%28-1%29%3D%28-1%29%5E2-8%2A%28-1%29%2B19%3D1%2B8%2B19%3D28+%5C%5C+y%284%29%3D4%5E2-8%2A4%2B19%3D16-32%2B19%3D3+%5C%5C+y%285%29%3D5%5E2-8%2A5%2B19%3D25-40%2B19%3D4+%5C%5C+y_%7Bmin%7D+%3Dy%284%29%3D3%3B+y_%7Bmax%7D%3Dy%28-1%29%3D28)
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![y=x^2+4x-3 \\ y'=2x+4 \\ 2x+4=0 \\ x=-2 \\ y(0)=-3 \\ y(2)=2^2+4*2-3=4+8-3=9 \\ y_{min}=y(0)=-3;y_{max}=y(2)=9 y=x^2+4x-3 \\ y'=2x+4 \\ 2x+4=0 \\ x=-2 \\ y(0)=-3 \\ y(2)=2^2+4*2-3=4+8-3=9 \\ y_{min}=y(0)=-3;y_{max}=y(2)=9](https://tex.z-dn.net/?f=y%3Dx%5E2%2B4x-3+%5C%5C+y%27%3D2x%2B4+%5C%5C+2x%2B4%3D0+%5C%5C+x%3D-2+%5C%5C+y%280%29%3D-3+%5C%5C+y%282%29%3D2%5E2%2B4%2A2-3%3D4%2B8-3%3D9+%5C%5C+y_%7Bmin%7D%3Dy%280%29%3D-3%3By_%7Bmax%7D%3Dy%282%29%3D9)
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![y=2x^2-8x+6 \\ y'=4x-8 \\ 4x-8=0 \\ x=2 \\ y(-1)=2*(-1)^2-8*(-1)+6=2+8+6=16 \\ y(2)=2*2^2-8*2+6=8-16+6=-2 \\ y(4)=2*4^2-8*4+6=32-32+6=6 \\ y_{min}=y(2)=-2; y_{max}=y(-1)=16 y=2x^2-8x+6 \\ y'=4x-8 \\ 4x-8=0 \\ x=2 \\ y(-1)=2*(-1)^2-8*(-1)+6=2+8+6=16 \\ y(2)=2*2^2-8*2+6=8-16+6=-2 \\ y(4)=2*4^2-8*4+6=32-32+6=6 \\ y_{min}=y(2)=-2; y_{max}=y(-1)=16](https://tex.z-dn.net/?f=y%3D2x%5E2-8x%2B6+%5C%5C+y%27%3D4x-8+%5C%5C+4x-8%3D0+%5C%5C+x%3D2+%5C%5C+y%28-1%29%3D2%2A%28-1%29%5E2-8%2A%28-1%29%2B6%3D2%2B8%2B6%3D16+%5C%5C+y%282%29%3D2%2A2%5E2-8%2A2%2B6%3D8-16%2B6%3D-2+%5C%5C+y%284%29%3D2%2A4%5E2-8%2A4%2B6%3D32-32%2B6%3D6+%5C%5C+y_%7Bmin%7D%3Dy%282%29%3D-2%3B+y_%7Bmax%7D%3Dy%28-1%29%3D16)
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![y=-3x^2+6x-10 \\ y'=-6x+6 \\ -6x+6=0 \\ x= 1 \\ y(-2)=-3*(-2)^2+6*(-2)-10=-12-12-10=-32 \\ y(1)=-3*1^2+6*1-10=-3+6-10=-7 \\ y(9)=-3*9^2+6*9-10=-243+54-10=-199 \\ y_{min}=y(9)=-199;y_{max}=y(1)=-7 y=-3x^2+6x-10 \\ y'=-6x+6 \\ -6x+6=0 \\ x= 1 \\ y(-2)=-3*(-2)^2+6*(-2)-10=-12-12-10=-32 \\ y(1)=-3*1^2+6*1-10=-3+6-10=-7 \\ y(9)=-3*9^2+6*9-10=-243+54-10=-199 \\ y_{min}=y(9)=-199;y_{max}=y(1)=-7](https://tex.z-dn.net/?f=y%3D-3x%5E2%2B6x-10+%5C%5C+y%27%3D-6x%2B6+%5C%5C+-6x%2B6%3D0+%5C%5C+x%3D+1+%5C%5C+y%28-2%29%3D-3%2A%28-2%29%5E2%2B6%2A%28-2%29-10%3D-12-12-10%3D-32+%5C%5C+y%281%29%3D-3%2A1%5E2%2B6%2A1-10%3D-3%2B6-10%3D-7+%5C%5C+y%289%29%3D-3%2A9%5E2%2B6%2A9-10%3D-243%2B54-10%3D-199+%5C%5C+y_%7Bmin%7D%3Dy%289%29%3D-199%3By_%7Bmax%7D%3Dy%281%29%3D-7)
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