Question

How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for `f(x) = (x - 1)/x`?

Answer 1

You need its derivative in order to know that.

Explanation:

If we want to know everything about `f`, we need `f'`.

Here, `f'(x) = (x-x+1)/x^2 = 1/x^2`. This function is always strictly positive on `RR` without `0` so your function is strictly increasing on `]-oo,0[` and strictly growing on `]0,+oo[`.

It does have a minima on `]-oo,0[`, it's `1` (even though it doesn't reach this value) and it has a maxima on `]0,+oo[`, it's also `1`.