Our slope of our original function is increasing, and we are concave upwards. So notice, we do indeed, the second derivative does indeed cross the x-axis at x equals negative two. It's not enough for it to just be zero or touch the x-axis. It needs to cross the x-axis in order for us to have an inflection point there. So given that, let's look at the students' justifications and see what we could, if we kind of put the teacher hat in our mind and say what a teacher would say for the different justifications. So the first student says the second derivative of g changes signs at x equals negative two. Well, that's exactly what we were just talking about.