Now find the minimum of I with respect to the position d. (ie. Take the derivative of I with respect to d, set it equal to 0, and solve for d. Then you need to show that this value of d is, in fact, a minimum point rather than a maximum.)
Warning: You are going to have to solve an ugly cubic equation. Don't even bother trying to factor it: I'd recommend a numerical solution. For reference, I'm getting d around 4.09 ft.