8 problems.
- A quadratic difference bound forces constancy — Assignment 8 Problem 1; exact canonical appearance of Rudin Exercise 5.1
- A function differentiable at exactly one point — Problem 2
- Continuity and differentiability of \(x^a\) and \(x^a\sin(1/x)\) at 0 — Problem 3
- Differentiability of sums and products of non-differentiable functions — Problem 4
- Zeros of functions with nonvanishing second derivative and the roots of \(x^2-\sin x\) — Problem 5
- Taylor remainder estimates for \(e^x\) and \(\sqrt{1+x}\) — Problem 6
- Uniform differentiability is equivalent to continuity of \(f'\) — Assignment 8 Math 6100 Bonus Problem 1; exact canonical uniformly-differentiable problem
- Universal chord theorem — Bonus problem 2