Question

c) using the graphs of ( f ) and ( f ), indicate where ( f ) is increasing and decreasing. give your answer in the form of an interval. note: when using interval notation in webwork, remember that: you use inf for ( infty ) and -inf for ( -infty ), 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 $f'$

A function $f(x)$ is increasing when $f'(x)> 0$ and decreasing when $f'(x)<0$.

Step2: Analyze the graph of $f'$

We need to look at the x - values for which the graph of $f'$ is above the x - axis (for increasing) and below the x - axis (for decreasing). Since the graphs of $f$ and $f'$ are not provided in a way that we can directly read off values, assume we had a proper graph of $f'$. If the graph of $f'$ is above the x - axis on an interval $(a,b)$, then $f$ is increasing on $(a,b)$. If the graph of $f'$ is below the x - axis on an interval $(c,d)$, then $f$ is decreasing on $(c,d)$.

Answer:

Since the actual graphs of $f$ and $f'$ are not fully legible and no specific numerical values can be determined from the provided image, we cannot give a specific interval answer. But the general process is as described above. If we had a proper graph of $f'$ with clear x - intercepts and regions above/below the x - axis, we would write the intervals for increasing and decreasing accordingly. For example, if $f'$ is positive on $(-\infty, 2)\cup(4,\infty)$ and negative on $(2,4)$, then $f$ is increasing on $(-\infty, 2)\cup(4,\infty)$ and decreasing on $(2,4)$.