Mean Value Theorem
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- Опубликовано: 25 авг 2024
- This calculus video tutorial provides a basic introduction into the mean value theorem. It contains plenty of examples and practice problems that show you how to find the value of c in the closed interval [a,b] that satisfies the mean value theorem. For the mean value theorem to be applied to a function, you need to make sure the function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).
Introduction to Limits:
• Calculus 1 - Introduct...
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
_____________________________
Extreme Value Theorem:
• Extreme Value Theorem
Finding Critical Numbers:
• Finding Critical Numbers
Local Maximum & Minimum:
• Finding Local Maximum ...
Absolute Extrema:
• Finding Absolute Maxim...
Rolle's Theorem:
• Rolle's Theorem
________________________________
Mean Value Theorem:
• Mean Value Theorem
Increasing and Decreasing Functions:
• Increasing and Decreas...
First Derivative Test:
• First Derivative Test
Concavity & Inflection Points:
• Concavity, Inflection ...
Second Derivative Test:
• Second Derivative Test
_________________________________
L'Hopital's Rule:
• L'hopital's rule
Curve Sketching With Derivatives:
• Curve Sketching - Grap...
Newton's Method:
• Newton's Method
Optimization Problems:
• Optimization Problems ...
_______________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ruclips.net/video/Dyl7jPlJXOM/видео.html
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2:00 - 2:23
4:44 MVT helps us to find a value (c) in between points (a) and (b), where the gradient(m) of tangent line == the m of the secant line (line touching a & b)
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Aprendi em 20 minutos em uma língua que não falo mais do que meu professor em meu idioma. Obrigado
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Am really grateful this tutorial has helped me alot my instructor is the worst maths teacher .... He acts like it's so difficult to learn
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can you please explain more or make atleast one vedeo on the ways of knowing how the graph wil look like by just looking at the eqns given
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Try f(x) = tanx on the interval [-Pi/2, Pi/2] to deduce that
|b - a| ≥ |tan(b) - tan(a)| where a & b belong to (-Pi/2, Pi/2)
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14:28 Determining whether function is continous on closed interval, open interval, and then determining whether MVT can be used
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How to know whether it is differentiable at certain close or open interval?
same question here
Well he mentioned that if a graph has a sharp turn then it's not differentiable at that point.
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Any way to know if a function isn't differentiable without plotting a graph?
I think you would have to have a function and then find domain restrictions such as a 0 in the denominator or if there is negative number in the square root
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Is there a way to determine if a function is continuous and/or differentiable w/o having to draw out a sketch graph?
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I don't understand how he got the graphs. Is there a video that I could watch the explains it all?
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Can there be two mean values in a given interval?
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If we change the interval to [2, 3] for
f(x) = |4x - 5|, then we can apply the MVT and we find f'(x) = 4 = [f(3) - f(2)]/[3 - 2]
So, 4 = [|7| - |3|]/[3 - 2] = 4.
This is true.
But what value of c satisfies this condition?
All c in (0, 4) according to the MVT and as it so happens in this case for c = 2 and c = 3 as well.