Finding Absolute Maximum and Minimum Values - Absolute Extrema

This calculus video tutorial explains how to find the absolute maximum and minimum values of a function on a closed interval. Tto find the absolute extrema, you need to find the relative extrema by finding the first derivative of the function and the critical numbers. Plot the critical numbers on a number line to create sign chart. Using the sign chart and the first derivative test, determine what type of relative extrema is present - if it's a relative maximum or a relative minimum. Next, place the critical numbers and the endpoints of the closed interval into an x y data table and compare the y values. The absolute maximum contains highest y value and the absolute minimum has the lowest y value.
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

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/gnncnmR3h8hlmac

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[@tshegofatsopreciousmapholo4380]

I am sorry but with the first problem you did, the sign line with 2 as a critical point, all the intervals were positive, none were negative, or have I just always done it wrong?

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Then we do have a relative extrema

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You went from 1+1 to extrema +b - c power of 3 mill and square rooted by 69 Im failing my test tomorrow and when my teacher explains its like he’s talking another language 😢

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[@Randude14]

THANK YOU SO MUCH. I was so confused on my homework between the difference of absolute and relative values.

[@acsas5973]

One of the most straightforward and informative videos out there on this topic. Very helpful thank you!

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[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you once again for another excellent review of Absolute Extrema, which is part of Calculus One. I really understand this video from start to finish. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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[@Titilomelirifa]

The first example is a parabola whose concavity is pointing upwards, therefore shouldnt it only have an abs/relative min and no max?

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[@khalidibrahim722]

This was so helpful very understanding but what if you something like x⁵-20x²

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[@nathanreyc]

How the FCK IS THE 1ST EXAMPLE SO SHIRT BUT The 2nd EXAMPLE is so fπzken long ?!?!? I hate math wtf I'ma fail so bad.

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[@drewpetersen3683]

Thank you!! You explained this topic very well!

[@hirokanakzawa6429]

Im a bit lost. Why do you leave the (x-5) after canceling out the top (x-5) for the second example?

[@Nupator]

it depends which one he picks (-3 or 6) (ITHINK!)

[@hariharan3085]

VERY GOOD EXPLANATION THANK U

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Your lessons are even better than my University Calculus lectures

[@karnmattu3586]

I have a question f(x)=x^3+6x^2 in the interval [-6,1]. This has minimums at (0,0) and (-6,0) what is the absolute minimum though

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[@nicholasmaloof8378]

So, critical points are always relative maxima/minima. Endpoints *can* be absolute maxima/minima, but *cannot* be relative maxima/minima. Critical points can sometimes be both the absolute and relative maxima/minima. Correct? XD

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[@R.T.17389]

Facts

Hello! What if I have more than critical point?

[@JKMath]

Hi! If you have more than one critical point, you will want to check the y-values of both critical points and compare them to each other as well as the endpoints of the interval. If you want to see some examples of this, I have several examples in my own video on this topic that may be able to help you! I will link it here for you. And if you have any further questions, feel free to leave a comment on the video, I would happy to answer them for you! Have a great day :) Link: kzbin.info/www/bejne/lYHcaIisfrh9ock

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[@BillyBob-tr5cv]

You see, the problem for me isn’t solving it out but simply finding out if it’s differentiable or not. I know it’s the most important and most simple step, but I just seem to mess it up each time. This video was helpful in the sense of reassuring that I’m doing polynomials right, but do you have any other videos where you do harder problems? Like trig or fractions or ones with double chain rules. Those are the suckers that get me.

[@supreetsingh987]

He has a differentiation vid with harder problems. Also look up derivative calculator and you should find a calculator that will calculate the derivative and show you the steps to get there.

[@sm__akash]

For the last one, why (1,57) and (6,2) will not be the local maximum and local minimum respectively

[@covenantslayergaming6362]

6 months late, hope this helps- x=3/2 comes out with y=62.75, which is larger than x=1 where y=57 thus making x=3/2 the local maximum. x=5 comes out with y=-23, which is lower than x=6 where y=2 thus making x=5 the local minimum. Cheers!

[@sm__akash]

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The derivative of my knowledge is positive

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Thank you! Hopefully my quiz questions are as easy as this

[@ortegaseanmichael9705]

may I know where did you get 6 as a divisor at 8:30?

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[@duyduc6293]

1:11 Isn't the local minimum at a?

[@JKMath]

Unlike absolute max and min, there can be more than one relative/local minimum and maximum. So yes, a would also be a local minimum you are correct!

[@eggxecution]

10:10, w8 how wre you able to factor out x-5 when you divide it by x-5? What rule is that, how is that possible??? Is it different from solving linear equation? Pls help!

[@andrewa.8516]

That factoring method is called the AC method which u can look up how it works

[@alimahmoud7082]

There is an easier way, you can open the calculator and press mode then 5 then 3 it will give you a, b, c put in a the coefficient of ×*2 and in b the coefficient of × and in c the free term and you will get the critical point quicker..

[@mrcordell9325]

Im in college and I really need help on this..

[@MelindaIrene-cmy0821]

I don't understand that what's derivative means like how does x2-4x+9 becomes 2x-4

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[@eggxecution]

Also what's the difference between relative minimum and max wit absolute min and max? How'd you know the difference between them pls help!

[@leg35nds15]

Dont know if you still need this answered but, relative max and min can be retrieved from your sign chart of the 2nd derivative, and absolute max/min is the highest max and the lowest min you have on the graph, and that is determined by using the given interval and plugging in the values of x to get y.

[@spyzzxg4m3rz7]

A guy on KZbin does the thing better than my masters teacher, thank you so much.

[@zahraaa59676]

The question you gave was too hard when it came to finding its zeroes, really set me back. Giving such unnecessarily big numbers was very annoying. But your method was very straightforward and clear, and I was able to put it into simple steps that I wrote down on my notes. Just wished I could have been able to try solving the problem myself as well.

[@appleitree]

In those cases a calculator is recommended because he said he calculated using a calculator. We don't usually have as much time in figuring out all these.

[@uncannyvalley3190]

My problem is that my pre-cal professor won't let me solve these extrema questions using derivatives. He requires that I solve it without them so I don't know how

[@ReetKashera_]

Superb Explanation 👍🏻👍🏻

[@marianablancoruiz1893]

I have a question how do you get the absolute value like in the second exersice you said there were [1,6] whay how??

[@PP-M_]

So, what about infinite intervals? Because it seems like I can't find anyone talking about it.

[@faisalmohamed4595]

I still don't understand how in 16:03 the relative max isn't 57!??! And why is the same as absolute

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This is very random but I would love to see someone with your knowledge take a final test for calculus 1 and just to see how easy you make it look as if it was just doing 1+1 and also how fast you could do it. That would be sick to see

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why cant we just make a delta and find c from -b-+sqrt delta // 2a its so much faster and less confusing

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3:54 he made a smily winking man!

[@KW-wr3xv]

At 6:04 how can it be both an absolute and relative min? Even with the closed interval, it is still just a parabola opening up so there would be no relative extrema.

[@stariaa_]

thank you for this it was really helpful

[@kerviskArt]

Wait… so if I were to look at a graph of f. The smallest y value is the absolute minimum?

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Why is the relative/local max and min the same as the abs max/min? Explain using the table

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Dude help me from algebra all the way to Calculus where I'm at now

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[@mkvpoopra]

when you plugged in did u ignore the exponents? you did 1x4 and didnt cube it?

[@laszloharangozo7971]

Thanks. This helped A LOT

[@trillshii]

7:50 What do you do when a coefficient is a prime number?

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Thank you so much. I'm so relieved now.

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Thank you 🙏

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[@farahela]

Thank you for the videos, one question at Minute (6:15) is f(1)=6 a local maximum, too?

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Thanks from the bottom of my heart ❤️

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thank you so much !!!!! I learn more from you in minutes than I do in my hour and a half calculus class. five minutes in I now know how to complete the rest of my homework !!! I can't tell you how many times this has happened to me.

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