Just look at the physics! Not the first derivatives or the N(d1). there are two extrema - (1) S =1, K = 99, T = 1mo... this option is worthless and will expire worthless. It has no sensitivity to S, i.e. the delta = 0. (2) S =999, K = 99, T = 1mo. This option will be exercised, you are going to own ...