Examples of Continuous and Differentiable Functions

	A function that is not continuous at any point in R
	A function that is continuous at the irrational numbers and discontinuous at the rational numbers.
	A function that is differentiable, but the derivative is not continuous.
	A function that is n-times differentiable, but not (n+1)-times differentiable
	A function that is not zero, infinitely often differentiable, but the n-th derivative at zero is always zero.
	A function that is continuous everywhere and nowhere differentiable in R.
	A continuous, non-constant, differentiable function whose derivative is zero everywhere except on a set of length zero.