> but if you asked me to explain what I'm doing I wouldn't be able to tell you, at least not using mathematical constructs/words That can come later, the more

> but if you asked me to explain what I'm doing I wouldn't be able to tell you, at least not using mathematical constructs/words That can come later, the more important point is to explain "why" you are doing a specific step and not "what" and you are free to use just English words. For example, say you want to find the maximum of f(x)= -x^2 + 4 x + 10. A bad explanation would be some mumbling about taking down the 2, ... , f'(x) =-2x +4, so x=2, f''(x)=-2, is negative, done. Better: We know that at a maximum the slope of f has to be zero (otherwise we could go left or right to get larger), so let's find such points first. We thus compute the derivative function as f'(x)=-2x+4 and find that it is zero if x=2. But that does not give an answer yet, because it could still be a min/max or saddle point. .. draw a small picture of each. We thus compute the second derivative to see in which of these three cases we might be. f'(x)=-2 is negative so we locally look like a parabola opened downward, so this is indeed a maximum.