Find derivatives from the left and from the right?

Question

What does that mean? Does that mean that we're to plug in something from the left and then something from the right to get two values or is there some complex way to do it that my teacher decided not to share with us? The problems I'm asking about specifically are:
find the derivatives from the left and form the right at x=1 (if they exist). Is the funcion differentiable at x=1?
53. f(x) = abs(x-1)
55. f(x) = (x-1)^3, x less than or equal to 1
(x-1)^2, x > 1

thanks for the help

Answer 1

The derivative form the left means you have to fing the limit

lim (h --> 0-) (f(x +h) - f(x))/h, and from the right

lim (h --> 0+-) (f(x +h) - f(x))/h

In the case of abs(x -1), the derivative from the left at x =1 is -1 and from the right is 1.

Answer 2

are you sure it didnt ask for the right and left hand limits?