Question

True or false: All continuous functions have derivatives

Answer 1

FALSE

Answer 2

Lets say you had f(x) =│x│

Answer 3

See?

Answer 4

\[\sum_{n=0} ^\infty a^n \cos(b^n \pi x)\]

where \(0<a<1\), \(b\) is a positive odd integer, and

\[ab > 1+\frac{3}{2} \pi.\]

;)

Answer 5

http://en.wikipedia.org/wiki/Weierstrass_function
Weierstrass function:
Continuous everywhere, differentiable nowhere :D