When we describe where the function is increasing, decreasing, and constant, we write open intervals written in terms of the x-values where the function is increasing or decreasing.

x values get larger, so do the y values or the function values. In a decreasing function; as the values get larger, the y values (function values) get smaller. Using ‘algebra’ language, the definitions of increasi

Problem This is useful, but if we want a complete description of when a function is growing, decreasing, or staying the same it seems like that we would have to plug every point into the derivative and …

f (x) increases on (−∞, −2], decreases on [−2, 1], and decreases on (1, ∞). Loc max: x = −2. Loc min: x = 1. Remark: f is not decreasing on ∞), [−2, even though it is decreasing on [−2, 1] and on (1, ∞) …

Find the critical numbers of f(x). Determine the intervals where f(x) is increasing and where f(x) is decreasing.

2) Determine the sign of f 0(x) on each interval from (1) and use the Test for Increasing and Decreasing Intervals to determine the open intervals on which f is increasing or decreasing. ex. Given f (x) = x3 3 …

In technical terms, the function f ( x ) = x 2 is decreasing on the interval − ∞ < x < 0 , has a minimum at (0, 0), and is increasing on the interval 0 < x < ∞ .