点p(2,f2)处的切线方程为y=x-1,
说明P点在直线上,故有:f(2)=2-1=1
而f(2)=8-4a+2+b,即:
8-4a+2+b=1 (1)
导数:f'(x)=3x^2-2ax+1
f'(2)=3*4-4a+1=1 (2)
(1)(2)两式联立得:
a=b=3
f(x)=x^3-3x^2+x+3
点p(2,f2)处的切线方程为y=x-1,
说明P点在直线上,故有:f(2)=2-1=1
而f(2)=8-4a+2+b,即:
8-4a+2+b=1 (1)
导数:f'(x)=3x^2-2ax+1
f'(2)=3*4-4a+1=1 (2)
(1)(2)两式联立得:
a=b=3
f(x)=x^3-3x^2+x+3