I simply cannot tell you how fed up I am with stupid mainstream academics - they are truly the bane of my existence. So the crap described here: https://en.wikipedia.org/wiki/Fundamental_increment_lemma has NOTHING to do with my historic theorem: https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020 The Holy Grail of Calculus: https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus If I had indeed copied the bullshit from the Wiki link, I would be as wrong as those fools who administer the shit pile known as Wikipedia. It is COMPLETELY WRONG in the "lemma" to say: "The lemma asserts that the existence of this derivative f'(a) implies the existence of a function phi(h)..." because the function Q(x,h) exists IF AND ONLY IF, the function f is SMOOTH throughout the interval. You cannot talk about one point and then assume it is true for the entire interval. I claimed my theorem based on the assumption that f is smooth over the given interval. Moreover, everything you learn about derivatives and limits in mainstream calculus is just a load of rubbish. Even the ubiquitous definition of derivative in terms of limits is a joke because it REQUIRES that a function be SMOOTH about a point where it supposes there is a derivative, but this is entirely circular, since all finite differences that converge to the slope of the tangent line must exist. Ironically, the finite difference which matters most, that is, the tangent line slope at the required point DOES NOT exist - EVER! It is only assumed in terms of a "limit" - that bullshit circular concept which crept into calculus with the likes of idiots such as Augustin Cauchy and others. Here is an applet where you can see that my theorem is true for ANY smooth function, unlike that troll and liar Markus Klyver has been claiming that it only works for polynomials. It works for ALL smooth functions. The troll simply spreads lies on sci.math and everywhere else where the psychopath obsessed with me stalks my articles and videos. He recently followed me on Academia.edu but I blocked the scum bag. There is no reason to give an ignoramus access to pearls of knowledge, rather let him die in his ignorance. https://drive.google.com/file/d/1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv Don't believe me! Prove that what I am telling you is true. I have given you ALL the information. You have no excuse to be an ignoramus, especially if you are a math professor or teacher. This video is aimed at YOU, MORON! I was the first human to define area and volume generally in terms of a general formula. Any area = product of two arithmetic means. Any volume = product of three arithmetic means. I have shown these facts to be true in single and multi-variable calculus, including surfaces where a normal vector is used to represent an area. Want to get instant updates for the newest math around? Join our discord server! https://discord.gg/CJ9Ks3WerR Merchandise Store: https://new-calculus.printify.me/products ... https://www.youtube.com/watch?v=mDQxAWWGGN8