Question

Why isn't the function f(x)=lxl differentiable at 0?

Answer 1

Because there is a corner. The derivative is different from the left-side and the right-side.

Answer 2

it is -1 on the left and 1 on the right, so at 0 it is not differentiable

Answer 3

what exactly does it mean to be differentiable?

Answer 4

It basically means that you can find the slope of the equation at that point. You can take the derivative at that point. Since the slope coming from the left is different than the slope coming from the right, that point on the graph is not diferentiable.

Answer 5

Alright, makes sense. thank you!

Answer 6

No problem

Answer 7

\[\lim x-> \infty of (\sqrt{x^2 +4x} - \sqrt{x^2-5x})\]