Answer:
When we have a function f(x), the values of x at which the function is not differentiable are:
1) values at which the function is not "soft". So if we have a really abrupt change in the curvature of the function, we can not differentiate in that value of x, because in those abrupt changes there are a lot of tangent lines to them.
One example of this is the peak we can see at x = -4
Then we can not differentiate the function at x = -4
2) When we have a discontinuity.
If we have a discontinuity at x = x0, then we will have two possible tangents at x = x0, this means taht we can not differentiate at x = x0, and remember that a discontinuity at x = x0 means that:
f(x0₊) ≠ f(x0₋)
where x0₊ is a value that approaches x0 from above, and x0₋ is a value that approaches x0 from below.
With this in mind, we can see in the graph a discontinuity at x = 0, so we can not differentiate the function at x = 0.
