Question

How to find instantaneous rate of change for `f(x) = ln(x)` when x=0?

Answer 1

`f'(x) = 1/x -> f'(0) = 1/0 = 0`

The instantaneous rate of change is `0`.

Explanation:

The instantaneous rate of change is also defined as the derivative, so all we're asked to do is to take a derivative using some essentials rules, such as the the following:

`d/dx[ln u] = (u')/(u)`

Letting `u = x -> du = dx`, and so

`f'(x) = 1/x -> f'(0) = 1/0 = 0`

The instantaneous rate of change is, in this case, `0`.