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

 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.