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?

1 Answer
Dec 23, 2015

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.