❖ The Mean Value Theorem ❖

Learn about the Mean Value Theorem in Calculus with a Complete Step-by-Step Example!
In this video, we'll explore the Mean Value Theorem (MVT) in Calculus. We begin by graphically explaining what the theorem states and aim to convince you why this theorem might just be true, even without a formal proof. From there, we'll work through a complete example with all the steps:

Demonstrating that the function satisfies the continuity and differentiability requirements.
Finding all values in the specified interval that satisfy the Mean Value Theorem.
Breaking down the algebra and calculus involved to make it as approachable as possible.
There's a bit of algebra and calculus work involved, but nothing super terrible—I hope!

What You Will Learn:

The graphical interpretation of the Mean Value Theorem.
How to verify the conditions of continuity and differentiability for a function.
Step-by-step process to find values that satisfy the MVT in a given interval.
Tips to simplify complex algebra and calculus steps.

📚 Check out my book: 1001 Calculus Problems for Dummies for more practice!

👍 **If you find this video helpful, please like, share, and subscribe for more math tutorials!

Support My Work:

#Calculus #MeanValueTheorem #MVT #MathTutorial #PatrickJMT #DifferentialCalculus #Algebra #Continuity #Differentiability #Mathematics

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[patrickjmt]

yep, that is it!
you can think of the slope of the line connecting the endpoints as being the mean in the sense that it represents the average rate of change of the function on that interval.
it says there is a tangent line on the graph in that interval with the same average rate of change! so the instantaneous rate of change must equal the average rate of change!

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[patrickjmt]

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