Inverse Function Theorem (OBS)-1

This is the first of a series of 2+ lectures on Inverse Function Theorem. It motivates the result and an enterprising viewer can actually arrive at the statement by himself/herself. The first step is proved in this.

[dhivyandhivyan]

sound quality in both vedios are equally good sir.

[dhivyandhivyan]

glb||D(f(z)) (x2-x1)|| \leq ||f(x2) - f(x_2)|| for all z \in [x1, x2] is this statement true sir?. Suppose it is true then to prove f is 1-1 is very easy because if we assume x1 \neq x2 then we can easily prove f(x1) \neq f(x2).