Finding Local Maximum and Minimum Values of a Function - Relative Extrema

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-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

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[@IamKudos]

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?

[@aeb4865]

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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[@orca3588]

How would we write our answers if the given function is rational with asymptotes in its graph?

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Great video but what about trig fnc's?

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[@omarfish8940]

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?

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[@yungcraftgod6725]

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[@felistus3439]

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?

[@asmarterself2906]

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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[@hararybeast8650]

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?

[@RajeshGupta-gg6io]

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.

[@sammymwania5502]

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

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What about trigonometric functions?

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f(×)=ײ-2×+1/×-2 find local extreme value and interval of monotoncity

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[@killman384]

hi so whats the difference between local extrema and max and min pt.?

[@SDILUYNTsiu39fnd]

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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[@argelnovo3120]

i have a question why did 6x^2 gcf is 6 while 12x^3 gcf is 12 with a variable x

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If x=0, then f(x) =x³ will be ?

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who came here for there modules thats damn hard

[@notduy7391]

What is a derivative

[@nohackers2037]

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?

[@elite7585]

i wish i could help u but i've no idea

[@jbalvin8318]

On 4:00 how do you find the derivative of that number 2X^3

[@wahidnoori2259]

3*2x^2=6x^2

[@alimahmoud7082]

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

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The way say "derivative" is funny.

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