Rolle's Theorem Explained and Mean Value Theorem For Derivatives - Examples - Calculus
This calculus video tutorial explains the concept behind Rolle's Theorem and the Mean Value Theorem For Derivatives. This video contains plenty of examples and practice problems.
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:
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Rolles Theorem: - see if f(x) is continuous (no holes, asymptotes..etc [denom can’t be 0]) in the closed interval. - see if f(x) is différentiable. (derivative is continuous) in the open interval. - check that f(a) = f(b) then there is a point where the derivative is 0 (has a horizontal tangent) - take the derivative and write f’(c) solve for c, check if it’s in the interval. Mean value theorem: - must be continuous in [a,b] - must be différentiable at (a,b) - then f’(c) = f(b)-f(a) = b-a (slope of tangent line = slope of secant line)
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2 ай бұрын
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Жыл бұрын
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This is the best tutorial on rolle's and mean value theorem i have ever seen...Nice one
@TheOrganicChemistryTutor
7 жыл бұрын
Thanks
@millions2nette
7 жыл бұрын
IKR! My professor has no idea how to explain this stuff. He also didn't show any appropriate example problems...He just throws it on a test.
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6 жыл бұрын
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4 жыл бұрын
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22:33 MEAN VALUE THEOREM
@jameswright5880
5 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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3 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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3 жыл бұрын
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2 жыл бұрын
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3 ай бұрын
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20:14 thank you very much i needed an edge case like this one, I almost forgot about the open/closed interval thing having never encountered something this
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5 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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3 жыл бұрын
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3 жыл бұрын
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2 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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5 жыл бұрын
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Great source to understand tutorial on rolle's
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There is another way to solve a Mean Value Theorem for Derivatives. You can find what f(b) and f(a) equal by plugging them into f(x) via the x value. As you find f(a) and f(b), you then plug them into the equation f(b)-f(a)/b-a. Make sure that b and a are the intervals while f(b) and f(a) are what you found when you plugged b and a into f(x). As you find the value of f(b)-f(a)/b-a, set that value equal to the derivative of f(x), aka f'(x), then solve. What you should get is a simple value such as x=? which you would rewrite it C=? Note: ? is just a value you would get. However, it can vary in certain cases.
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so for the last problem, you had the square root which resulted in a pos and a neg number but the pos one was the right one because it was between -1 and 3. my question is what if both had been between -1 and 3. would they both be C or would you have to choose one?
im confused about 22:17. Underoot of (x-4) should mean that x cannot be equal to 3. Then y is it continous from 0 to 4
@IsaacDuran-hm2uy
6 ай бұрын
you are correct he made a mistake
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What if c is a complex number in mean value theorem
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im confused on the first MVT problem. where did the 4-0 go? is it not x=-3 ?
@CaseyMarkov
2 жыл бұрын
what was the time stamp for the problem?
@MysteriousMM4
Жыл бұрын
He multiplied both sides by 4 to cancel the denominator.
@Potato-so6zr
8 ай бұрын
@@MysteriousMM4because 4 - 0 is just 4
MVT 22:38 Rolle's Thm. Q: 13:34
@itskim9790
Жыл бұрын
" 20:14 thank you very much i needed an edge case like this one, I almost forgot about the open/closed interval thing having never encountered something this"
@itskim9790
Жыл бұрын
24:44
The derivative of his aging process must = 0
Explains better than my teacher
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