describe the behavior of the function by determining which intervals the function has a positivr average rate of change

Question

graph= starts at 0 goes up to 5,5 goes down to 3,8 goes up to 10,15

(1 point)
The average rate of change is positve over the interval [
,
] and over the interval [
,
].

Answer 1

To determine the intervals where the function has a positive average rate of change, we need to analyze the function's behavior based on the graph's description you provided:

1. The function starts at (0,0) and goes up to (5,5). This means it's increasing over the interval [0, 5], so the average rate of change is positive here.

2. The function then goes down from (5,5) to (3,3) during the interval [5, 8]. Since it is decreasing during this interval, the average rate of change is negative.

3. Next, the function increases again from (3,3) to (10,15) over the interval [8, 10]. This indicates it is increasing over this interval, hence the average rate of change is positive here as well.

Putting this all together:

• The average rate of change is positive over the intervals [0, 5] and [8, 10].

So, the answer is: The average rate of change is positive over the interval \([0, 5]\) and over the interval \([8, 10]\).