设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切…设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切.(1)求a、b的值.(2)求f(x)的单调区间.
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![设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切…设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切.(1)求a、b的值.(2)求f(x)的单调区间.](/uploads/image/z/8981995-67-5.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dx3-3ax%2Bb%28a+%E2%89%A00%29%E7%9A%84%E5%9B%BE%E5%83%8F%E5%9C%A8%E7%82%B9%281%2Cf%281%29%29%E5%A4%84%E4%B8%8E%E7%9B%B4%E7%BA%BFy%3D2%E7%9B%B8%E5%88%87%E2%80%A6%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dx3-3ax%2Bb%28a+%E2%89%A00%29%E7%9A%84%E5%9B%BE%E5%83%8F%E5%9C%A8%E7%82%B9%281%2Cf%281%29%29%E5%A4%84%E4%B8%8E%E7%9B%B4%E7%BA%BFy%3D2%E7%9B%B8%E5%88%87.%EF%BC%881%EF%BC%89%E6%B1%82a%E3%80%81b%E7%9A%84%E5%80%BC.%EF%BC%882%EF%BC%89%E6%B1%82f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4.)
设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切…设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切.(1)求a、b的值.(2)求f(x)的单调区间.
设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切…
设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切.
(1)求a、b的值.
(2)求f(x)的单调区间.
设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切…设函数f(x)=x3-3ax+b(a ≠0)的图像在点(1,f(1))处与直线y=2相切.(1)求a、b的值.(2)求f(x)的单调区间.
f‘(x)=3x^2-3a=3(x^2-a)
在f(1))与y=2相切,斜率k=0
f'(1)=3(1^2-a)=0
a=1
f(x)=x^3-3x+b
f(1)=2
3-3+b=2
b=2
f'(x)=3(x^2-1)=3(x+1)(x-1)
x∈(-∞,-1)单调增
x∈(-1,1)单调减
x∈(1,∞)单调增