设f(x)=x(x-1)(x-2)(x-3)(x-4),则f‘(0)=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 03:34:53
![设f(x)=x(x-1)(x-2)(x-3)(x-4),则f‘(0)=?](/uploads/image/z/9314490-66-0.jpg?t=%E8%AE%BEf%28x%29%3Dx%28x-1%29%28x-2%29%28x-3%29%28x-4%29%2C%E5%88%99f%E2%80%98%EF%BC%880%EF%BC%89%3D%3F)
设f(x)=x(x-1)(x-2)(x-3)(x-4),则f‘(0)=?
设f(x)=x(x-1)(x-2)(x-3)(x-4),则f‘(0)=?
设f(x)=x(x-1)(x-2)(x-3)(x-4),则f‘(0)=?
f'(x)=x'(x-1)(x-2)(x-3)(x-4)x(x-1)'(x-2)(x-3)(x-4)+x(x-1)(x-2)'(x-3)(x-4)+x(x-1)(x-2)(x-3)'(x-4)+x(x-1)(x-2)(x-3)(x-4)'
=(x-1)(x-2)(x-3)(x-4)+x(x-2)(x-3)(x-4)+x(x-1)(x-3)(x-4)+x(x-1)(x-2)(x-4)+x(x-1)(x-2)(x-3)
后面每项都有x,则x=0时等于0
所以f'(0)=4!=24
f(x)为5次多项式
f'(x)=ax^4+bx^3+cx^2+dx+e
f'(0)=e
e即为f(x)的一次项系数,
由于设f(x)=x(x-1)(x-2)(x-3)(x-4)
f(x)的一次项系数=1*2*3*4=24
f'(0)=24