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 …

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.

We analyze the intervals of increasing/decreasing y-values for the function by dy determining where dx is positive and where it is negative.

Example 1: Find the intervals on which f(x) = 2x3 +9x2+12x is increasing and the intervals on which it is decreasing. Last time we saw that relative extrema of a function can occur at points where the …

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.

Determine the interval(s) where f(x) is decreasing. Determine the interval(s) where f(x) is concave up. Determine the value(s) of x where f(x) has relative (local) extrema. Classify each as the location of a …