Question

已知函数f（x）=x三次方 +bx二次方+cx+2在x等于一处取得极值-1,求b,c

Answer 1

f(x)=x³+bx²+cx+2

f'(x)=3x²+2bx+c

x=1时f(x)=-1 ==> 1+b+c+2=-1 ==> b+c=-4

x=1时f'(x)=0 ==> 3+2b+c=0 ==> 2b+c=-3

解得 b=1,c=-5