The correct option is C (1,73]
We have, f(x)=x2+x+2x2+x+1=(x2+x+1)+1x2+x+1=1+1(x+12)2+34
We can see here that as x→∞,f(x)→1, which is the min value of f(x). Also f(x) is max when (x+12)2+34 is min which is so when x=−12 and then 34.
∴ fmax=1+134=73
∴ Ri=(1,73]