Function with POSITIVE DERIVATIVE but DECREASES!

If you're interested in personal help, I've posted my tutoring services on Fiverr: https://www.fiverr.com/s/dDYkBlz I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to do some online tutoring. In this video, we give an example of a function which is differentiable everywhere with positive derivative, but the function decreases. In kindergarten, we learn about increasing and decreasing functions, and their relationship with the derivative. We typically learn that a function with positive derivative increases, while a function with negative derivative decreases. But is this always the case? Well, it turns out to not always be the case, and this video works through an example of such. This fun math example, is something anyone studying high school mathematics can understand, but it is perhaps best suited to those who have just finished a first course in analysis. Timestamps: 0:00 T.W. Körner quote 0:13 Introductory chit chat 1:10 T. W. Körner's book -- A Companion to Analysis 2:58 The example of a function with a positive slope but decreases 3:15 Proof that the function is differentiable with positive derivative everywhere 5:14 Proof that the function decreases 5:54 Summary of what we've shown 6:54 Outro chit chat 👍 To support the channel, hit the like button and subscribe. 🐸 To learn how I make these animations using Grant Sanderson's (3Blue1Brown) program Manim, check out my quick intro to Manim on Skillshare: https://www.skillshare.com/r/profile/Kyle-B/344454857 🎸 Music in this video is from Epidemic Sound: https://www.epidemicsound.com/referral/yi0wzw/ Ways to support the channel: 🏆 Support the channel over on Patreon https://www.patreon.com/KyleBroder 🐸 Support the channel by signing up to a free-trial of Skillshare using the link https://www.skillshare.com/r/profile/Kyle-B/344454857 FYI, these are affiliate links 💪🙏 These videos are separate from my research and teaching roles at the Australian National University, University of Sydney, and Beijing University. These videos are made using the open-source library -- Manim -- created by 3blue1brown: https://github.com/3b1b/manim