Calculus | Polynomial functions
In mathematics, a cubic function is a function of the form where the coefficients a, b, c, and d are complex numbers, and the variable x takes real values, and . In other words, it is both a polynomial function of degree three, and a real function. In particular, the domain and the codomain are the set of the real numbers. Setting f(x) = 0 produces a cubic equation of the form whose solutions are called roots of the function. A cubic function has either one or three real roots (which may not be distinct); all odd-degree polynomials have at least one real root. The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum. Otherwise, a cubic function is monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half turn around this point. Up to an affine transformation, there are only three possible graphs for cubic functions. Cubic functions are fundamental for cubic interpolation. (Wikipedia).
Solving Cubic Inequalities (1 of 3: Interpreting the graph)
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From playlist Further Work with Functions
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From playlist Graphing Functions (Algebra 1)
How to write the equation of a cubic function given the graph
👉 Learn how to identify transformations of functions. Transformation of a function involves alterations to the graph of the parent function. The transformations can be dilations, translations (shifts), reflection, stretches, shrinks, etc. To sketch the graph of a transformed function, we s
From playlist Characteristics of Functions
Define linear functions. Use function notation to evaluate linear functions. Learn to identify linear function from data, graphs, and equations.
From playlist Algebra 1
Introduction to Linear Functions and Slope (L10.1)
This lesson introduces linear functions, describes the behavior of linear function, and explains how to determine the slope of a line given two points. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Introduction to Functions: Function Basics
How to write the inverse of a power function
👉 Learn how to find the inverse of a cubic function. A cubic function is a function whose highest exponent in the variable(s) of the function is 3. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of a functi
From playlist Find the Inverse of a Function
Graphing Cubic Functions (1 of 4: Considering y = x³)
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From playlist Working with Functions
Ex 2: Solve a Cubic Function Graphically (Two Solutions)
This video explains how to solve a cubic equation graphically using the intersections of two functions. http://mathispower4u.com
From playlist Determining the Characteristics of Polynomial Functions
Statistical Learning: 7.2 Piecewise Polynomials and Splines
Statistical Learning, featuring Deep Learning, Survival Analysis and Multiple Testing You are able to take Statistical Learning as an online course on EdX, and you are able to choose a verified path and get a certificate for its completion: https://www.edx.org/course/statistical-learning
From playlist Statistical Learning
Counting Low Degree Number Fields with Almost Prescribed Successive Minima - Sameera Vemulapalli
Joint IAS/PU Number Theory Seminar Topic: Counting Low Degree Number Fields with Almost Prescribed Successive Minima Speaker: Sameera Vemulapalli Affiliation: Princeton University Date: January 26, 2023 The successive minima of an order in a degree n number field are n real numbers encod
From playlist Mathematics
Lec 19 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 19: Quadratic/cubic elements License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
Mod-01 Lec-08 Cubic Spline Interpolation
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
CTNT 2020 - Non-vanishing for cubic L-functions - Alexandra Florea
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
algebraic geometry 27 The twisted cubic
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes two examples: the twisted cubic is isomorphic to a projective line, and the affine plane without the origin is not isomorphic to any affine algebraic set.
From playlist Algebraic geometry I: Varieties
Solutions to Cubic Equations - Benedict Gross (Harvard University)
Beginning with some simple principles that go back to the ancient Greeks for solving some low-degree equations, we will then turn to some basic questions raised by Euler and Fermat, whose answers have led to surprising applications (secure Internet commerce) as well as to the solution of f
From playlist Mathematics Research Center
Solving Cubic Equations - Benedict Gross
Speaker : Benedict Gross Date and Time : 06 Jan 12, 17:15 Venue : AG 66, TIFR, Mumbai I will discuss a problem which has been central in number theory for several centuries -- whether a cubic equation in the plane has infinitely many rational solutions.This led to a precise conjecture by
From playlist Public Lectures
Lec 21 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 21: Boundary conditions, splines, gradient and divergence (part 1) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
Define a linear function. Determine if a linear function is increasing or decreasing. Interpret linear function models. Determine linear functions. Site: http://mathispower4u.com
From playlist Introduction to Functions: Function Basics