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The question asks about the Mean Value Theorem (MVT) in relation to water levels recorded from November 2 to November 7.

### The Mean Value Theorem (MVT) states:
If a function \( f(x) \) is continuous on the closed interval \([a, b]\) and differentiable on the open interval \((a, b)\), then there exists at least one point \( c \in (a, b) \) such that:
\[
f'(c) = \frac{f(b) - f(a)}{b - a}
\]
This means there is a point in the interval where the instantaneous rate of change (slope of the tangent) equals the average rate of change over the entire interval.

### Now, applying this to the problem:
- From Nov 2 to Nov 7, the water level changed from **23.5 meters** to **19.5 meters**, over **5 days**.
- The average rate of change (slope) is:
\[
\text{Average rate} = \frac{19.5 - 23.5}{7 - 2} = \frac{-4}{5} = -\frac{4}{5} \text{ meters per day}
\]
So, according to the Mean Value Theorem, at some point between Nov 2 and Nov 7, the water level must have been decreasing at exactly \( -\frac{4}{5} \) meters per day.

### Correct Answer:
**A.** "At some moment in time between November 2 and November 7, the water level was decreasing at a rate of exactly \( \frac{4}{5} \) meters per day."

Would you like further clarification on the Mean Value Theorem or how it applies here?

Here are 5 related questions you might want to explore:
1. How does the Mean Value Theorem apply to real-world phenomena like temperature change?
2. Could the Mean Value Theorem be applied to non-linear functions?
3. What happens if a function is not continuous or differentiable over the interval?
4. How does the instantaneous rate of change relate to the overall behavior of a function?
5. What are some other practical uses of the Mean Value Theorem in engineering or physics?

**Tip:** When using the Mean Value Theorem, always ensure the function meets the conditions of continuity and differentiability over the interval.

What does the Mean Value Theorem allow you to conclude over the time period from November 2 to November 7 given the water levels recorded at the Glenmore Reservoir?

Learn how the Mean Value Theorem applies to real-world problems with a detailed solution for water level changes in the Glenmore Reservoir between November 2 and November 7. Discover the rate of change calculations and how to find a point where the instantaneous rate equals the average rate of change. Suitable for high school students studying calculus.

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