Question

Y= { x if x<_0 , 2x if x>_ 0 } find if y is differentiable at 0 .Then, if y is differentiable find the derivative at x=0.

Y’ = { 1 if x < 0 ,2 if x >0 } How do you continue from here?

Answer 1

Since
y' = 1 for x <= 0
y' = 2 for x>0
y' is not continuous at x=9. So, y is not differentiable there.
Whenever you have a cusp or point on a graph, the function is not differentiable there.
Better reread the definition of differentiable.

Answer 2

It is looking for y to be differentiable at 0. I think I understand because it is not continuous at x=0.