设函数f(x)=1/3x^3-a/2x^2+bx+c,其中a>0,曲线y=f(x)在点P(0,f(0))处的切线方程为y=1(1)确定b,c的值(2)设曲线y=f(x)在点(x1,f(x1))及(x2,f(x2))处的切线都过点(0,2)证明:当x1不等于x2时,f’(x1)不等于f
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![设函数f(x)=1/3x^3-a/2x^2+bx+c,其中a>0,曲线y=f(x)在点P(0,f(0))处的切线方程为y=1(1)确定b,c的值(2)设曲线y=f(x)在点(x1,f(x1))及(x2,f(x2))处的切线都过点(0,2)证明:当x1不等于x2时,f’(x1)不等于f](/uploads/image/z/5497286-14-6.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D1%2F3x%5E3-a%2F2x%5E2%2Bbx%2Bc%2C%E5%85%B6%E4%B8%ADa%3E0%2C%E6%9B%B2%E7%BA%BFy%3Df%28x%29%E5%9C%A8%E7%82%B9P%EF%BC%880%2Cf%280%29%EF%BC%89%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%E4%B8%BAy%3D1%281%29%E7%A1%AE%E5%AE%9Ab%2Cc%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%AE%BE%E6%9B%B2%E7%BA%BFy%3Df%28x%29%E5%9C%A8%E7%82%B9%EF%BC%88x1%2Cf%28x1%29%29%E5%8F%8A%EF%BC%88x2%2Cf%28x2%29%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E9%83%BD%E8%BF%87%E7%82%B9%EF%BC%880%2C2%EF%BC%89%E8%AF%81%E6%98%8E%EF%BC%9A%E5%BD%93x1%E4%B8%8D%E7%AD%89%E4%BA%8Ex2%E6%97%B6%2Cf%E2%80%99%28x1%EF%BC%89%E4%B8%8D%E7%AD%89%E4%BA%8Ef)
设函数f(x)=1/3x^3-a/2x^2+bx+c,其中a>0,曲线y=f(x)在点P(0,f(0))处的切线方程为y=1(1)确定b,c的值(2)设曲线y=f(x)在点(x1,f(x1))及(x2,f(x2))处的切线都过点(0,2)证明:当x1不等于x2时,f’(x1)不等于f
设函数f(x)=1/3x^3-a/2x^2+bx+c,其中a>0,曲线y=f(x)在点P(0,f(0))处的切线方程为y=1
(1)确定b,c的值
(2)设曲线y=f(x)在点(x1,f(x1))及(x2,f(x2))处的切线都过点(0,2)证明:当x1不等于x2时,f’(x1)不等于f’(x2)
(3)若过点(0,2)可做曲线y=f(x)的三条不同的切线,求a的取值范围
设函数f(x)=1/3x^3-a/2x^2+bx+c,其中a>0,曲线y=f(x)在点P(0,f(0))处的切线方程为y=1(1)确定b,c的值(2)设曲线y=f(x)在点(x1,f(x1))及(x2,f(x2))处的切线都过点(0,2)证明:当x1不等于x2时,f’(x1)不等于f
由题干可知,f(x)过点(0,1),在x=0处的切线斜率为0,即f’(0)=0
(1)f’(x)=x^2-ax+b(a>0)
列出方程组:f’(0)=b=0
f(x)=c=1
解得b=0,c=1
(2)设曲线y=f(x)在点(x1,f(x1))及(x2,f(x2))处的切线的斜率分别为k1,k2
k1=f’(x1)=x1^2-ax1+b
k2=f’(x2)=x2^2-ax2+b
设两切线分别为y1=k1x+b1,y2=k2x+b2
因为两切线都过点(0,2)
所以b1=b2=2
(-∞,1/2)∪(5,+∞)
撒旦啊