the question is find the points of inflection of f(x) = 1/2x^4+x^3+6x^2-2x-4

now my understanding is that to find points of inflection, i would need to find the 2nd derivative first, right?

this is what i have for the 2nd D - 6x^2+6x+12. then you would factor so 6(x^2+x+2), i can't really go on after this because you can't really factor it out, right? so there is points of inflection for this equation? i am guessing there is not...?