Mean Value Theorem Example

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High school math teacher explains an Example using the Mean Value Theorem of Calculus!

In order to apply The Mean Value Theorem, make sure these two conditions are met:
1) f is continuous on the closed interval [a,b]
2) f is differentiable on the open interval (a,b)

As long as these conditions are met, The Mean Value Theorem guarantees there exists a number c in (a,b) such that f'(c)=[f(b)-f(a)]/(b-a) OR where the instantaneous rate of change (IROC) = the average rate of change (AROC).

Thank you for watching! Please comment below about any questions or comments you have!
  1. Calculus by Christee
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  3. calculus
  4. calculus by christee
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Great video!!! The laying out of the two conditions was awesome at the start since so many students jump right to the calculations even in invalid cases where there may be a hole, an asymptote, or a sharp turn in the graph. I also LOVE how you took the time to mention how this was a special case of Rolle's Theorem - I feel like a lot of people feel these concepts are disconnected and you clearly showed here that Rolle's is just one specific situation of the MVT! This goes back to your central focus of understanding over memorization and that is awesome! Lastly, the reminder at the end of the problem about sticking to the provided interval was super helpful - I've had lots of students in the past give too many solutions (e.g. in this case they would've also given 3pi/2) since they didn't read the question carefully. Great tips all around in this video! Always look forward to your videos for great tips, explanations, and new perspectives of looking at problems. This MVT video was an MVT - most valuable tutorial! 😁👍

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