Question

c) using the graphs of f and f, indicate where f is increasing and decreasing. give your answer in the note: when using interval notation in webwork, remember that: you use inf for ∞ and -inf for −∞, and use u for the union symbol. enter dne if an answer does not exist. f is increasing on f is decreasing on

Explanation:

Step1: Recall the relationship between $f$ and $f'$

If $f'(x)>0$ on an interval, then $f(x)$ is increasing on that interval. If $f'(x)<0$ on an interval, then $f(x)$ is decreasing on that interval.

Step2: Analyze the sign of $f'$ from the graph

Since the graphs of $f$ and $f'$ are not provided separately in a way to clearly identify $f'$'s sign regions, assume we can visually estimate. If the slope of the tangent - line to the graph of $y = f(x)$ is positive, $f$ is increasing. If the slope of the tangent - line to the graph of $y = f(x)$ is negative, $f$ is decreasing.

Answer:

Since no specific graphs of $f$ and $f'$ are given in a usable form to determine the intervals precisely, we cannot provide a numerical answer. If we assume we had the correct graphs:
Let the intervals where $f'(x)>0$ be $I_1,I_2,\cdots$. Then $f$ is increasing on $I_1\cup I_2\cup\cdots$. Let the intervals where $f'(x)<0$ be $J_1,J_2,\cdots$. Then $f$ is decreasing on $J_1\cup J_2\cup\cdots$. But without the actual visual analysis of the correct $f$ and $f'$ graphs, we enter DNE for both the increasing and decreasing intervals.
$f$ is increasing on DNE
$f$ is decreasing on DNE