Finding Local Maximum and Minimum Values of a Function - Relative Extrema
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- Опубликовано: 25 авг 2024
- This calculus video tutorial explains how to find the local maximum and minimum values of a function. In order to determine the relative extrema, you need to find the first derivative, set it equal to zero, and solve for x which represents the critical numbers of the function. You need to put these numbers on a number line and create a sign chart. According to the first derivative test, if the sign changes from - to +, it's a relative maximum. If it changes from + to -, it's a relative minimum. This video contains plenty of examples and practice problems for you to work on.
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
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my calc class got moved online bc of corona. this channel is literally my teacher. how did people ever learn math from a book?
Edgar Moreno same here honestly I should’ve watch this guy sooner
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You've got a very bad philosophy towards Calculus. One might not "learn math from a book" because you are not interested at the subject! Never insult books! They are like people. You treat them properly they reward you! Doing the opposite would make you suffer!
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Math is supposed to be taught not just said out loud
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Hello you know I have spent a whole year in the university understanding the local maxima and local minima and I always fail !!!! Really I don’t know how to thank you ,I have exam after few days and you have ease my life !? You are amazing and great and the best tutor in this whole world please keep up and also post videos on statistic this channel has to get a golden reward
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By far the best video out there: quick, simple, straight-to-the-point. It helped me greatly! Thank you!
Thank for you video! The lecture notes use many many words to explain this concept that made me confuse about it, while you use some simple examples to explain it clearly!!
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started watching this since my finals for basic calculus is tomorrow
"decreasin' and increasin'"
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Professor Organic Chemistry Tutor, thank you for a solid analysis and a step-by-step explanation of Finding the Relative Extrema/Max/Min Values in Calculus. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
i thought it was difficult but he makes it simple
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Thank you this was very helpful and well explained.
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when he's doing your exact problem
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I understand why you're asking (curiosity), but really think for a moment - how would showing his face be beneficial to him at all? None of his videos are about him, they are about math. Also, why would it matter what his face looks like? It shouldn't matter what he looks like. To be honest, the only reason anyone would want to see him do a "face reveal" is due to curiosity. Let's be real here: that's not a good enough reason for him to do it. There just isn't a good case for it. It's pointless.
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But in the last example, if we plug in f(2), we get y=16, so we do get a coordinate (2,16) and that could've been the relative maximum point if we used functions to do so. But theoretically we can see that it doesn't have a relative maximum point. How do we explain that with the functions method if we are asked to show our work?
I know you probably got it by now but commenting for future people, as far as I could understand it’s because it’s a double root so if you were to graph the derivative it’d look like a parabola shaping upwards. That point is a point of inflection rather than a critical point where the second derivative changes signs, changing the concavity of the function
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the second example is literally the hw question I was stuck on lmao
Nice sir I can understand
It's really a good explanation
The description is inaccurate: where you say "f the sign changes from - to +, it's a relative maximum." should be minimum instead of maximum; same goes for + to -, for a relative maximum.
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hi so whats the difference between local extrema and max and min pt.?
extrema and max, and minima and min are the same. Just different ways of saying it.
local means that the point it within a interval like [1,9] so the local min/minima is the lowest point in the interval where d/dx(fx) = 0. (slope is 0)
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Great video but what about trig fnc's?
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The multiplicity stuff is confusing
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f(×)=ײ-2×+1/×-2 find local extreme value and interval of monotoncity
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How would we write our answers if the given function is rational with asymptotes in its graph?
He plugged 1 and -1 for the last example, wouldn't they both be positive? as -1-3 = -4 and you square that which is positive cause he did the same for 1 when he did 1-3 = -2 but he then squared it which would make it positive.
Thanku sir ✨🙂
i have a question why did 6x^2 gcf is 6 while 12x^3 gcf is 12 with a variable x
when finding the y value, on the first one we used the f(x)' then substituted the x values......but why did we use f(x) on the second example instead of f(x)' again?
for the f(x) 3x^4-16x^3+24x^2 I don't understand why the critical number couldn't just stay x=2 why do we have to solve for 12x=0 when we didn't in the other problems. I dont know if this is a stupid question I just think I might be over think it, can anyone help me?
MY HERO
Hello how do we find maxima and minima of trigonometric functions for example what is the minima and maxima of the following function y=sin(x³/3- x²/2-2x+1) this is really enormous problem to me
13:30 how would we determine which is the shape of the curve?
I'm currently thinking that it might be taking the 2nd derivative of a function and seeing how the shape of the function changes from that point. Would that be it or am I completely off?
If x=0, then f(x) =x³ will be ?
What about trigonometric functions?
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What is a derivative
Can you do it in reverse? Have 2 local max and min (eg 4, 8 and -1,-2)
I tried. x=4 x-4 x= -1 x+1
x(x-1)+4(x-1)
x^2 -3x -4
3(x^2) -(3)(3x) -3(4)
3x^2 -9x -12
6x -9
6(4) -9 is minimum (which shouldn't so...)
Or
-x = -4 -x +4 -x = 1 -x-1
-x(-x-1)+4(-x-1)
-x^2 +3x +4
-3(x^2) +9x +12
-x^3 +4.5x^2 +12x +- c
-4^3 + 4.5(4)^2 + 12(4) +- c = 9
-(-1)^3 + 4.5(-1)^2 + 12(-1) +- c = -2
C = 47
C = -4.5 WHAT DID I DO WRONG?
i wish i could help u but i've no idea
On 4:00 how do you find the derivative of that number 2X^3
3*2x^2=6x^2
The power goes down then do a [ - 1] from the power so it will be (2) so it will be 3 × 2×*2 then it will be 6×*2
im stuck on something likes this
y=(e^(x)+e^(-x))/(2)
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