Question

函數(shù)f(x)=x³+bx²+cx+d的大致圖象如圖所示,則+等于(　　)

A．

B．

C．

D．

Answer 1

C

【思路點(diǎn)撥】從函數(shù)圖象上可知x₁,x₂為函數(shù)f(x)的極值點(diǎn),故x₁,x₂是f'(x)=0的兩根,再根據(jù)根與系數(shù)的關(guān)系進(jìn)行求解.
解:從函數(shù)圖象上可知x₁,x₂為函數(shù)f(x)的極值點(diǎn),根據(jù)函數(shù)圖象經(jīng)過(guò)的三個(gè)特殊點(diǎn)求出b,c,d.根據(jù)函數(shù)圖象得d=0,且f(-1)=-1+b-c=0,f(2)=8+4b+2c=0,解得b=-1,c=-2,故f'(x)=3x²-2x-2,所以x₁+x₂=,x₁x₂=-,所以+=(x₁+x₂)²-2x₁x₂=+=.