Differentiability of sums and products of non-differentiable functions

Exactly one of the following requests is impossible. Decide which it is, and provide examples for the other three. In each case, lets assume that the functions are defined on all of R.

1. Function \(f\) and g not differentiable at \(x _ { 0 } = 0\) , but where \(f g\) is differentiable at \(x _ { 0 } = 0\)

2. A function f not differentiable at \(x _ { 0 } = 0\) and a function g differentiable at \(x _ { 0 } = 0\) where \(f g\) is differentiable at \(x _ { 0 } = 0\)

3. A function f not differentiable at \(x _ { 0 } = 0\) and a function \(g\) differentiable at \(x _ { 0 } = 0\) where \(f + g\) is differentiable at \(x _ { 0 } = 0\)

4. A function \(f\) differentiable at \(x _ { 0 } = 0\) , but not differentiable at any other point.