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Μάθημα: Διαφορικός Λογισμός > Ενότητα 5
Μάθημα 1: Mean value theorem- Mean value theorem
- Mean value theorem example: polynomial
- Mean value theorem example: square root function
- Χρησιμοποιώντας το Θεώρημα Μέσης Τιμής
- Establishing differentiability for MVT
- Justification with the mean value theorem
- Mean value theorem application
- Mean value theorem review
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Mean value theorem review
Review your knowledge of the mean value theorem and use it to solve problems.
What is the mean value theorem?
The mean value theorem connects the average rate of change of a function to its derivative. It says that for any differentiable function and an interval (within the domain of ), there exists a number within such that is equal to the function's average rate of change over .
Graphically, the theorem says that for any arc between two endpoints, there's a point at which the tangent to the arc is parallel to the secant through its endpoints.
Want to learn more about the mean value theorem? Check out this video.
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