Question

已知f（x）=ax²+bx+c，且f（-1）=2，f′（0）=0，f（x）dx=-2，求a、b、c的值.

Answer 1

a=6,b=0,c=-4

解析:

  由f（-1）=2，得a-b+c=2，                                                     ①

又f′(x)=2ax+b,

由f′(0)=0得b=0,                                                                  ②

f(x)dx=(ax²+bx+c)dx

=(ax³+x²+cx)|

=a+b+c.

即a+b+c=-2，                                                                             ③

由①②③得：a=6,b=0,c=-4.