Questions: Use the graph of f to find the largest open interval on which f is increasing, and the largest open interval on which f is decreasing. (Enter your answers using interval notation.)
(a) Find the largest open interval(s) on which f is increasing. (If two open intervals are equally large enter your answer as a comma-separated list of intervals.)
(b) Find the largest open interval(s) on which f is decreasing. (If two open intervals are equally large enter your answer as a comma-separated list of intervals.)
Transcript text: Use the graph of $f$ to find the largest open interval on which $f$ is increasing, and the largest open interval on which $f$ is decreasing. (Enter your answers using interval notation.)
(a) Find the largest open interval(s) on which $f$ is increasing. (If two open intervals are equally large enter your answer as a comma-separated list of intervals.)
(b) Find the largest open interval(s) on which $f$ is decreasing. (If two open intervals are equally large enter your answer as a comma-separated list of intervals.)
Solution
Solution Steps
Step 1: Identify the increasing interval
The function is increasing where the y-value increases as the x-value increases. Looking at the graph, this occurs between x = 4 and x = 5.
Step 2: Write the increasing interval in interval notation
The function is increasing on the open interval (4, 5).
Step 3: Identify the decreasing intervals
The function is decreasing where the y-value decreases as the x-value increases. This occurs in two separate intervals on the graph: between x = 1 and x = 4, and between x = 5 and x = 6.
Step 4: Determine the largest decreasing interval
The interval from 1 to 4 is a length of 3, and the interval from 5 to 6 is a length of 1. Thus, the largest decreasing interval is (1, 4).