Question
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Find the average rate of change of on the interval . Your answer will be an
expression involving

Ask by Rose Weaver. in the United States
Jan 29,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The average rate of change of on the interval is .

Solution

The average rate of change of a function over the interval is given by:
For the function on the interval :
  1. Calculate and :
  2. Compute the difference :
  3. Divide by the interval length :
  4. Simplify the expression:
Final Answer:

Reviewed and approved by the UpStudy tutoring team

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Simplify this solution

The Deep Dive

To find the average rate of change of the function on the interval , we can use the formula for the average rate of change, which is given by:
First, we calculate :
Next, we compute :
Now, substituting these values into the average rate of change formula gives us:
Simplifying the numerator:
So we have:
We can factor the numerator:
Therefore, the expression simplifies to:
For , this simplifies to:
Thus, the average rate of change of on the interval is:

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