Cauchy's Mean Value Theorem: Visual Proof (DTube)

Recently I was asked whether I could go over a visual proof of the Cauchy's Mean Value Theorem, as I had done for the Lagrange or simple version of the Mean Value Theorem (MFT). This was a very interesting question so I decided to go ahead and go over the graphical visualization of the theorem. In this video I show that the Cauchy or general mean value theorem can be graphically represented in the same way as for the simple MFT. The only difference is that the horizontal axis is not x, but a more general function of x, g(x). This difference causes the formulation to be more general, and the instantaneous slope to be formulated in the more general definition of the derivative, as shown in my last video. This is a very interesting topic to understand, but make sure to watch my earlier video on the general definition of derivative to get a better understanding of this!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtgYCYyHYoceOBojYA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/cauchy-s-mean-value-theorem-visual-proof