Differential calculus | Functions and mappings | Mathematical analysis | Linear operators in calculus
In calculus, the second derivative, or the second order derivative, of a function f is the derivative of the derivative of f. Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of an object with respect to time is the instantaneous acceleration of the object, or the rate at which the velocity of the object is changing with respect to time. In Leibniz notation: where a is acceleration, v is velocity, t is time, x is position, and d is the instantaneous "delta" or change. The last expression is the second derivative of position (x) with respect to time. On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the opposite way. (Wikipedia).
Second Derivative of Vector-Valued Function Example 1
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From playlist Calculus
Second Derivative of Vector-Valued Function Example 2
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From playlist Calculus
The true second derivative test
In this video I present the second derivative test in multivariable calculus, which is used to find local maxima/minima/saddle points of a function. However, unlike the nonsense they usually teach in the books, here I'm presenting a more elegant way with some linear algebra blended in. I'm
From playlist Partial Derivatives
Using the Second Derivative (1 of 5: Finding the Point of Inflexion)
More resources available at www.misterwootube.com
From playlist Applications of Differentiation
Section (4.2) Second Derivatives and Graphs
Applied Calculus Section (4.2) Second Derivative and Graphs In this lecture the second derivative is defined as it relates to the first derivative and as it relates to the graph of the original function. The second derivative is used in graphical analysis to identify intervals of concavity
From playlist Applied Calculus
The Second Derivative (1 of 3: Introducing Terminology)
More resources available at www.misterwootube.com
From playlist Applications of Differentiation
Calculus: The Second Derivative Test
In this video, we learn about the second derivative and how it can be used to classify extreme function values.
From playlist Calculus
The Second Derivative of Parametric Equations - Part 1 of 2
Complete Video List: http://www.mathispower4u.yolasite.com This video explains how to determine the second derivative of parametric equations and how to determine when a curve written in parametric form is concave up or concave down.
From playlist Parametric Equations
Second derivative test: two variables
Free ebook http://tinyurl.com/EngMathYT A lecture on the 2nd derivative test for multivariable calculus. The ideas are illustrated through examples. I also provide a proof of the 2nd derivative test.
From playlist Mathematics for Finance & Actuarial Studies 2
Concavity Inflection Second Derivative Test 4 Examples Calculus 1 AB
Visual Analysis 4:23 Examples at 21:40 29:47 42:16 Even though this is corrected, I still forgot the power of 2 on the cosine in the denominator at minute 46:41 I have a full set of notes for Concavity: Testing for Concavity, Look at some graphical examples of where concavity may change
From playlist Calculus
Applied Calc 1 Ep 21: Second derivative test
Episode 21 of my videos for my Applied Calculus 1 course at Fairfield University. This is a first calculus course for undergraduates, taken mostly by business and health/life sciences students. This episode is about the second derivative test. Class webpage: http://cstaecker.fairfield.ed
From playlist Math 1121 (Applied Calculus 1)
Worldwide Calculus: Higher-Order Derivatives
Lecture on 'Higher-Order Derivatives' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Applied Calc 1 Ep 20: Higher derivatives
Episode 20 of my videos for my Applied Calculus 1 course at Fairfield University. This is a first calculus course for undergraduates, taken mostly by business and health/life sciences students. This episode is about higher derivatives. Class webpage: http://cstaecker.fairfield.edu/~cstae
From playlist Math 1121 (Applied Calculus 1)
Applied Calc 1, Episode 20: 2nd derivative test
Episode 20 of my videos for my "flipped" Math 119 (Applied Calculus 1) course from Spring 2015 at Fairfield University. This is a first calculus course for undergraduates, taken mostly by business and health/life sciences students. This episode is about using the second derivative to iden
From playlist Math 119 (Applied Calc I) Fall 2017
Calculus AB Homework 4.5: Second Derivative Test
Download Packet: https://goo.gl/tg9SDC ================================= AP Calculus AB / IB Math SL Unit 4: Applications of the Derivative Lesson 5: Second Derivative Test for Concavity =================================
From playlist AP Calculus AB
Partial derivatives - How to solve?
► My Partial Derivatives course: https://www.kristakingmath.com/partial-derivatives-course Partial derivatives are just like regular derivatives, but for multivariable functions. We’re used to taking the derivative of a single variable function, which is simple because we just take the de
From playlist Calculus III
Worldwide Calculus: Multivariable Taylor Polynomials and Series
Lecture on 'Multivariable Taylor Polynomials and Series' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Derivatives
Checking Solutions in Differential Equations (Differential Equations 3)
https://www.patreon.com/ProfessorLeonard Determining whether or not an equation is a solution to a Differential Equation.
From playlist Differential Equations
Applied Calc 1, Episode 19: Higher derivatives
Episode 19 of my videos for my "flipped" Math 119 (Applied Calculus 1) course from Spring 2015 at Fairfield University. This is a first calculus course for undergraduates, taken mostly by business and health/life sciences students. This episode is about higher derivatives and concavity.
From playlist Math 119 (Applied Calc I) Fall 2017
Calculus 3: Partial Derivative (10 of 30) Find the 2nd Partial Derivative
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the 2nd partial derivative with-respect-to x and y of f(x,y)=(x^2)+(y^3)-4x+6y+4. Next video in the series can be seen at: https://youtu.be/gGTipvy1lPU
From playlist CALCULUS 3 CH 4 PARTIAL DERIVATIVES