函数f(x)=x^3+ax^2+bx+c和g(x)=4x^2-7x+2满足下列两个条件,求abc的值1f(x)在x=-1处有极值2曲线y=f(x)和y=g(x)在(2,4)处有公切线

Question

函数f(x)=x^3+ax^2+bx+c和g(x)=4x^2-7x+2满足下列两个条件,求abc的值
1f(x)在x=-1处有极值
2曲线y=f(x)和y=g(x)在(2,4)处有公切线

Answer 1

f'(x)=3x^2+2ax+b 在x=-1有极值可得：
3-2a+b=0``````````````````````````````1
g'(x)=8x-7曲线y=f(x)和y=g(x)在(2,4)处有公切线
可得：
f(2)=g(2)=4 可得：
8+4a+2b+c=4````````````````````````2
f'(2)=g'(2)可得：
12+4a+b=16-7``````````````````````3
联立1、2、3解得：a=0,b=-3,c=2