设函数F(X)=x^3-3ax+b(a不等于0)1)若曲线y=f(x)在点(2,f(x))处与直线y=8相切(2)当a0时,求函数f(x)的单调区间与极值点
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![设函数F(X)=x^3-3ax+b(a不等于0)1)若曲线y=f(x)在点(2,f(x))处与直线y=8相切(2)当a0时,求函数f(x)的单调区间与极值点](/uploads/image/z/2997340-52-0.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0F%28X%29%3Dx%5E3-3ax%2Bb%28a%E4%B8%8D%E7%AD%89%E4%BA%8E0%EF%BC%891%29%E8%8B%A5%E6%9B%B2%E7%BA%BFy%3Df%28x%29%E5%9C%A8%E7%82%B9%282%2Cf%28x%29%29%E5%A4%84%E4%B8%8E%E7%9B%B4%E7%BA%BFy%3D8%E7%9B%B8%E5%88%87%282%29%E5%BD%93a0%E6%97%B6%2C%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%E5%80%BC%E7%82%B9)
设函数F(X)=x^3-3ax+b(a不等于0)1)若曲线y=f(x)在点(2,f(x))处与直线y=8相切(2)当a0时,求函数f(x)的单调区间与极值点
设函数F(X)=x^3-3ax+b(a不等于0)
1)若曲线y=f(x)在点(2,f(x))处与直线y=8相切(2)当a<0时,求函数f(x)的单调区间(3)a>0时,求函数f(x)的单调区间与极值点
设函数F(X)=x^3-3ax+b(a不等于0)1)若曲线y=f(x)在点(2,f(x))处与直线y=8相切(2)当a0时,求函数f(x)的单调区间与极值点
1)f'(x)=3x^2-3a
在点(2,f(2))处与直线y=8相切, 则有f'(2)=0=12-3a, 得:a=4
且f(2)=8=8-3*4*2+b, 得:b=24
即f(x)=x^3-12x+24
2)a<0时,f'(x)=3(x^2-a)>0, 因此f(x)在R上都单调增
3)f'(x)=3(x^2-a),
a>0时,极值点为x=√a,-√a
单调增区间为:(-∞,-√a), (√a,+∞)
单调减区间为:(-√a, √a)
极大值f(-√a)=2a√a+b
极小值f(√a)=-2a√a+b
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