已知函数f(x)=x^3+3ax^2+3bx+c在x=2处有极值,其图象在x=1处的切线与直线6x+2y+5=0平行,求极大值和极小值的差f'(x)=3x^2+6ax+3bx=2时 12+12a+3b=0x=1时 3+6a+3b=-3解得a=-1 b=0所以f'(x)=3x^2-6x=3x(x-2)极大值:
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![已知函数f(x)=x^3+3ax^2+3bx+c在x=2处有极值,其图象在x=1处的切线与直线6x+2y+5=0平行,求极大值和极小值的差f'(x)=3x^2+6ax+3bx=2时 12+12a+3b=0x=1时 3+6a+3b=-3解得a=-1 b=0所以f'(x)=3x^2-6x=3x(x-2)极大值:](/uploads/image/z/3988401-33-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%5E3%2B3ax%5E2%2B3bx%2Bc%E5%9C%A8x%3D2%E5%A4%84%E6%9C%89%E6%9E%81%E5%80%BC%2C%E5%85%B6%E5%9B%BE%E8%B1%A1%E5%9C%A8x%3D1%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E4%B8%8E%E7%9B%B4%E7%BA%BF6x%2B2y%2B5%3D0%E5%B9%B3%E8%A1%8C%2C%E6%B1%82%E6%9E%81%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9E%81%E5%B0%8F%E5%80%BC%E7%9A%84%E5%B7%AEf%27%EF%BC%88x%EF%BC%89%3D3x%5E2%2B6ax%2B3bx%3D2%E6%97%B6+12%2B12a%2B3b%3D0x%3D1%E6%97%B6+3%2B6a%2B3b%3D-3%E8%A7%A3%E5%BE%97a%3D-1+b%3D0%E6%89%80%E4%BB%A5f%27%EF%BC%88x%EF%BC%89%3D3x%5E2-6x%3D3x%EF%BC%88x-2%EF%BC%89%E6%9E%81%E5%A4%A7%E5%80%BC%EF%BC%9A)
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