Question
Find the average rate of change of
on the interval
. Your answer will be an
expression involving
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
:
-
Calculate
and : -
Compute the difference
: -
Divide by the interval length
: -
Simplify the expression:
Final Answer:
Reviewed and approved by the UpStudy tutoring team
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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: