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

1 Answer
Alexander
Jul 13, 2016

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.

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