设函数f(x)=x^3-3ax^2+3bx的图像与直线12x+y-1=0相切于点(1,-11),(1)求a,b(2)讨论函数f(x)的单调性
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![设函数f(x)=x^3-3ax^2+3bx的图像与直线12x+y-1=0相切于点(1,-11),(1)求a,b(2)讨论函数f(x)的单调性](/uploads/image/z/6891979-67-9.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dx%5E3-3ax%5E2%2B3bx%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8E%E7%9B%B4%E7%BA%BF12x%2By-1%3D0%E7%9B%B8%E5%88%87%E4%BA%8E%E7%82%B9%281%2C-11%29%2C%281%29%E6%B1%82a%2Cb%282%29%E8%AE%A8%E8%AE%BA%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E6%80%A7)
设函数f(x)=x^3-3ax^2+3bx的图像与直线12x+y-1=0相切于点(1,-11),(1)求a,b(2)讨论函数f(x)的单调性
设函数f(x)=x^3-3ax^2+3bx的图像与直线12x+y-1=0相切于点(1,-11),(1)求a,b(2)讨论函数f(x)的单调性
设函数f(x)=x^3-3ax^2+3bx的图像与直线12x+y-1=0相切于点(1,-11),(1)求a,b(2)讨论函数f(x)的单调性
f(x)'=3x^2-6ax+3b 由题知 1-3a+3b=-11,3-6a+3b=-12,解之:a=1,b=-3;
(2).f(x)'=3x^2-6x-9,令f(x)'=0,解之,x=3,x=-1;所以当
x=3 ,f(x)单调增;当-1
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