Question

The graph of f is given. State the numbers at which f is not differentiable.​

Answer 1

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.