Extreme Value Theorem

This calculus video tutorial provides a basic introduction into the extreme value theorem which states a function will have a minimum and a maximum value on a closed interval. This video provides graphical examples of absolute extrema and relative extrema. It shows you how to identify the absolute maximum and minimum values of a function on a graph. It also explains how to identify the relative maximum and minimum values as well.
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:
/ collections

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/eKGcdpWMaKiCjKM Final Exams and Video Playlists: www.video-tutor.net/

[@SNIPE263]

Just wanted to say thanks for your videos man! They're super helpful and the way you explain is easy to follow. I can literally type in any concept and you've made a video for it. amazing!

[@Dmangames-gg3cl]

Love these videos. very helpful for night before cramming for calculus mid term

[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a solid explanation of the Extreme Value Theorem. This is another important theorem in Calculus/Advanced Calculus. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@krovely8649]

you are the best, you always have a video on literally anything I search

[@Sabineee3]

A question in my maths textbook told me to comment on "extreme values". So here I am!

[@Zenbeau]

you are DOING GOD's WORK. You have a video on everything that's in my first year uni calculus course

[@du42bz]

God 😂🤣

[@tiktokfunnycollection2626]

ደነዝ

[@faisalmohamed4595]

No one can do GOD's work

[@Zenbeau]

@faisalmohamed4595 it was a metaphor buddy know how English works?

[@faisalmohamed4595]

​@@Zenbeau man stfu i know english better than you

[@aguilarexequielandrew4758]

keep doing what youre doing! helps alot

[@suckmyhugewiener633]

love you organic chemistry tutor 💘

[@rodelynespinosa6311]

thank u so much u always save my life

[@ilkeuyankerstudent5347]

thankss

[@zeroblade8315]

question if u had a horizontal line at a closed interval[a,b] EVT says there should be a max and a min right, but there isn't one, in that case right?

[@just.a.guy522]

You could say that the minimum and the maximum values are the same, equal to the line's y value. Or you could also say that the EVT doesn't apply to constant functions.

[@zeroblade8315]

@@just.a.guy522 Alright thx

[@ahlam5915]

God bless ur mind

[@user-bu8mg7uq3s]

thank you

[@HDitzzDH]

5:30 Wouldn't f(d) be considered a local maximum since that is an endpoint?

[@therencehabon2916]

The graph isn't​ a closed interval

[@explorerofworlds512]

I think in this case it is a relative maximum that happens to also be the absolute maximum. I think of them as attributes or descriptions of the point that are not mutually exclusive. Think if it was a graph of temperature. Just because it's the hottest portion on the graph doesn't mean it is Not the hottest portion in its region in fact the hottest portion on the graph will inevitably also be the hottest portion of its region.

[@emmanuelssali6694]

Thanks a lot. But how would I tell if a graph contains open circles or closed circles?

[@kasm1488]

( ) this show it open, [] it show closed

[@felipenetto5646]

What if the function is for example y=1? it is continuous for every xER and it has neither max and mins

[@justmisu]

In those cases, the maximum and minimum are the same. The smallest value you can get is also the highest value possible

[@sustrata9125]

​@@justmisu could you say that it has neither min nor max?

[@azaa2188]

4:38 Reasoning for no absolute minimum on left graph: the interval isn't closed at points a and b. // a and b are at open intervals and therefore can't have absolute maximums or minimums. if a was a closed point, then it would be abs. minimum On right graph, b represents an abs minimum because it's lowest point AND has closed interval. C is not abs max, because its an open circle. 5:13 right graph, the EVT doesnt apply here because there is a break in the graph, therefore no closed interval

[@Humblemanvice]

❤

[@matthewkoob7600]

What a god.

[@kissmeok1004]

엑스바 어찌됨evt

[@explorerofworlds512]

Shouldn't this be called the definition of extreme values & not the extreme values? There's no proof you can make for this. It seems like we literally define relative mins & maxs values as points at which x equals 0 between an decreasing & increasing slope. We do the same for absolute max & min as the largest possible value of our function i.e if there is a maximum or minimum value to the function.

[@Humblemanvice]

Our Savior 😂

[@daizybaby1088]

really bad never understood anything from the video!!!! and never did

[@dontyouwonder]

this video was not very useful