Concept explainers
True or False? Justify your answer with a proof or a counterexample. Assume that f(x) is continuous and differentiable unless stated otherwise.
525. If
To check: whether the given data is true or false if
Answer to Problem 525RE
The statement is true.
Explanation of Solution
Given information:
The given data is
Then, there exists at least one point
Formula used:
Mean Value Theorem:
If
then there exists some
Calculation:
The given data is
Then, there exists at least one point
Here,
Thus, by the mean value theorem,
Therefore, by the mean value theorem the given statement is correct.
Conclusion:
Hence, the given statement is true.
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