Question
Problem 8:
Let
on the interval
.
. Apply the MVT to find the value(s) of
in
where
.
Let
. Apply the MVT to find the value(s) of
Ask by Lane Dawson. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The values of
in
that satisfy the Mean Value Theorem are
and
.
Solution

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The Deep Dive
To find the values of
using the Mean Value Theorem (MVT), we begin by calculating
and
.
First, we evaluate:
Next, we calculate
:
Now, we need to find
and set it equal to 8:
Calculating the derivative:
Setting
:
Now, we will use the quadratic formula,
:
Calculating the approximate values of these roots, we find:
Now, evaluating
, we calculate:
Since
needs to be in the interval
, both
and
are valid solutions. Thus, the values of
are approximately: