设函数f(x)=x3减3ax加b(a不等于0).(1)若曲线y=f(x)在点(2,f(2))处与直线y=8相切,求实数a,b的值.2)求函数f(x)的单调区间与极极值点
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![设函数f(x)=x3减3ax加b(a不等于0).(1)若曲线y=f(x)在点(2,f(2))处与直线y=8相切,求实数a,b的值.2)求函数f(x)的单调区间与极极值点](/uploads/image/z/8982054-54-4.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dx3%E5%87%8F3ax%E5%8A%A0b%28a%E4%B8%8D%E7%AD%89%E4%BA%8E0%29.%281%29%E8%8B%A5%E6%9B%B2%E7%BA%BFy%3Df%28x%29%E5%9C%A8%E7%82%B9%282%2Cf%282%29%29%E5%A4%84%E4%B8%8E%E7%9B%B4%E7%BA%BFy%3D8%E7%9B%B8%E5%88%87%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%2Cb%E7%9A%84%E5%80%BC.2%29%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%E4%B8%8E%E6%9E%81%E6%9E%81%E5%80%BC%E7%82%B9)
设函数f(x)=x3减3ax加b(a不等于0).(1)若曲线y=f(x)在点(2,f(2))处与直线y=8相切,求实数a,b的值.2)求函数f(x)的单调区间与极极值点
设函数f(x)=x3减3ax加b(a不等于0).(1)若曲线y=f(x)在点(2,f(2))处与直线y=8相切,求实数a,b的值.
2)求函数f(x)的单调区间与极极值点
设函数f(x)=x3减3ax加b(a不等于0).(1)若曲线y=f(x)在点(2,f(2))处与直线y=8相切,求实数a,b的值.2)求函数f(x)的单调区间与极极值点
f(x)=x³-3ax+b,则:
f'(x)=3x²-3a
(1)点(2,f(2))是切点,且这个点在直线y=8上,则:f(2)=8,则:
①f(2)=8-6a+b=8
②f'(2)=12-3a=0
解①、②,得:a=4,b=24
(2)f'(x)=3x²-12=3(x-2)(x+2)
得:f(x)在(-∞,-2)上递增,在(-2,2)上递减,在(2,+∞)上递增
函数f(x)的极值点是x=2或x=-2,极大值是f(-2),极小值是f(2)
(1)a=4,b=16
(2)单增区间(-无穷,2),(2,+无穷),单减区间(-2,2)
极大值点-2,极小值点2