Suppose you are given a formula for a function f. (a) how do you determine where f is increasing or decreasing

We can determine where f is increasing or decreasing based on the derivative f' (x).

If f' (x) > 0, the function is increasing.

If f' (x) < 0, the function is decreasing.

We'll solve those inequalities to find the intervals on which the function is increasing or decreasing.