设函数
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,其中a>0,曲线y=f(x)在点P(0,f(0))处的切线方程为y=1.
(Ⅰ)确定b,c的值;
(Ⅱ)设曲线y=f(x)在点(x
1,f(x
1))及(x
2,f(x
2))处的切线都过点(0,2).证明:当x
1≠x
2时,f′(x
1)≠f′(x
2);
(Ⅲ)若过点(0,2)可作曲线y=f(x)的三条不同切线,求a的取值范围.
考点分析:
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