Inflection Point of a Logistic Function

preview_player
Показать описание

  1. David Flenner
Рекомендации по теме
Inflection Point of 0:16:52

Inflection Point of a Logistic Function

Logistic Functions - 0:04:52

Logistic Functions - Coordinates of a Logistic Function's Inflection Point

Inflection Point Logistic 0:04:53

Inflection Point Logistic Functions

MAT1193 Lecture 11 0:10:01

MAT1193 Lecture 11 Inflection Points

MAT1193 4.2 Inflection 0:09:22

MAT1193 4.2 Inflection points

MATH1193 Logistic Growth 0:03:01

MATH1193 Logistic Growth Example

Point of Inflection 0:01:15

Point of Inflection

The Logistic Function 0:10:04

The Logistic Function 2: Sketching The S-Curve

MAT1193 Finding Inflection 0:04:40

MAT1193 Finding Inflection Points

Inflection Points - 0:01:18

Inflection Points - Manual for TI-84 Plus CE Graphing Calculator

Comprehensive Framework on 0:15:46

Comprehensive Framework on Inflection Points & Concavities

Corona Math - 0:22:06

Corona Math - Part II: Where's the Inflection Point?

Calculus 2, Ch 0:15:02

Calculus 2, Ch 6.4, the Logistic model

Fit an exponential 0:02:27

Fit an exponential regression and calculate the inflection point in Excel

5.4 Application of 0:09:19

5.4 Application of Differentiation exponential function: Extrema and inflection points

Calculus BC – 0:16:28

Calculus BC – 7.9 Logistic Models with Differential Equations

Business Calculus - 1:02:36

Business Calculus - Math 1329 - Section 3.2 - Concavity and Points of Inflection

Logistic Growth Curves 0:16:58

Logistic Growth Curves

Why do we 0:16:07

Why do we Care About Inflection Points? (Math 611B)

Worked example: Logistic 0:08:47

Worked example: Logistic model word problem | Differential equations | AP Calculus BC | Khan Academy

Section 4.2 - 0:05:49

Section 4.2 - Introduction to Inflection Points

4.4 Inflection Points 0:05:24

4.4 Inflection Points and Second Derivatives (part 1)

Reflecting on Inflection 0:10:19

Reflecting on Inflection Points using the Ti-Nspire

4.4 Inflection Points 0:43:49

4.4 Inflection Points and Second Derivatives (part 1)

Комментарии
Автор

Thank you so much! This video is the only thing that actually helped me.

alexisowen
Автор

I've noticed something: If we write the derivative of P(t) = M/(1+Ae^(-MKt)) as dP/dt = kP(M-P), where M is the carrying capacity, the inflection point occurs when the P value is half of the carrying capacity. You can see this by taking the second derivative, which is K(MKP(M-P)-2KP^2(M-P)). Set that to zero and we can get MKP(M-P)-2KP^2(M-P) = 0. From this, we get M/2P(M-P)-P^2(M-P) = 0. This means that M/2P(M-P) = P^2(M-P). We can cancel out the M-P term, leaving us with M/2P=P^2, and therefore P=M/2. Then, just plug in the P value into the original equation to solve for t. Do you think that this method is valid?

potatoman
Автор

or you can just set the function equal to half of its limiting value, in this case 50, and solve for x. It is much simpler that way.

DumbleDork