Question
*Homework 1.3 - Average rates of change of functions
Score:
Question 13
Find the average rate of change of
expression involving
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Score:
Question 13
Find the average rate of change of
expression involving
Question Help: Video
Submit Question
Ask by Johnson Hamilton. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The average rate of change of
Solution
To find the average rate of change of the function
Step 1: Calculate
First, we need to evaluate
Step 2: Calculate
Next, we evaluate
Step 3: Substitute into the average rate of change formula
Now we can substitute
Step 4: Simplify the expression
Now, let’s simplify the expression step by step.
-
Calculate
: -
Substitute
into the average rate of change formula: -
Simplify the numerator:
So, the average rate of change becomes:
Final Expression
Thus, the average rate of change of
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Simplify this solution Extra Insights
To find the average rate of change of the function
First, calculate
So, the average rate becomes:
Simplifying further will give the rate in terms of
Have you ever thought about how different functions behave similarly to cars on a road trip? When you’re cruising along a straight path, the speed (or rate of change) is consistent, but when you hit hills or curves, your speed changes—just like how the average rate lets us know the pace between two points on a curve!
In real-world scenarios, knowing the average rate of change can help in various fields. For instance, in economics, a company might analyze the average rate of change in revenue over time to predict future growth. Similarly, in physics, understanding average speed can help us design better transportation routes or even plan to save fuel!
