here we can write x³+x²+x+1 as (x⁴-1)/x-1

so f(x)=x⁴-1/x-1=

f'(x) = (x-1)4x³ - x⁴/(x-1)² = x³(4x-4-x)/(x-1)²=

x³(3x-4)/(x-1)²

again calculate {(x-1)²(16x³-12x²)  -(4x⁴-4x³)2(x-1)}/(x-1)⁴

 

put f'(x) =0  we get x=0,3/4 

 for x=0

f''(x) = 0

and x=3/4

we get f''(x) =

 

 

 

find this

after finding f''(x) for x=3/4 u can easily find out the answer.