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-tutor.net/
Full-Length Videos and Worksheets:
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Final Exams and Video Playlists: www.video-tutor.net/

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[@ayanaxhye]

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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22:33 MEAN VALUE THEOREM

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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

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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?

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Hey on the first part of the intro of mean value in the video . .. is it optional or me not to multiply both sides by 4 to get rid of the fraction of F(4)-F(0)/ 4-0 ? ?

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im confused on the first MVT problem. where did the 4-0 go? is it not x=-3 ?

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what was the time stamp for the problem?

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He multiplied both sides by 4 to cancel the denominator.

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(-3/2)^3 is -27/8 but then he distributed the 2 that was on the outside of the parenthesis because it was 2(-3/2)^3. That would give him -54/8. But we know that -54 is divisible by 2 because he would have just multiplied -27 by 2 to get -54. We also know that 8 is divisible by 2. So when you simplify -54/8, you get -27/4. He just skipped that step in the process of showing his work because that would have taken more time and more steps to show. So, instead of multiplying the numerator and then simplifying, he just divided the denominator by that 2 giving him the simplest form of that answer or term in one step instead of two steps.

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