Higher Order Derivatives. Find if. Substitute back into the equation.

Slides:

Advertisements

Similar presentations

Lesson 9 – Identities and roots of equations

Advertisements

AP Review Questions Chapters 1 – 4.

IB Studies Level Mathematics

Notes 6.6 Fundamental Theorem of Algebra

Mathematics for Economics Beatrice Venturi 1 Economics Faculty CONTINUOUS TIME: LINEAR DIFFERENTIAL EQUATIONS Economic Applications LESSON 2 prof. Beatrice.

Lesson 7-1 Integration by Parts.

EXAMPLE 1 Find the number of solutions or zeros

Shortcuts: Solution by Inspection for Two Special Cases A Lecture in ENGIANA AY 2014 – 2015.

Differential Equations Brannan Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 08: Series Solutions of Second Order Linear Equations.

F(x,y) = x 2 y + y y  f — = f x =  x 2xyx 2 + 3y y ln2 z = f(x,y) = cos(xy) + x cos 2 y – 3  f — = f y =  y  z —(x,y) =  x – y sin(xy)

Point Value : 20 Time limit : 2 min #1 Find. #1 Point Value : 30 Time limit : 2.5 min #2 Find.

Section 6.1 Cauchy-Euler Equation. THE CAUCHY-EULER EQUATION Any linear differential equation of the from where a n,..., a 0 are constants, is said to.

Modeling with Polynomial Functions

What is it and how do I know when I see it?

The Power Rule  If we are given a power function:  Then, we can find its derivative using the following shortcut rule, called the POWER RULE:

 Find the next three terms in each sequence:  5, 15, 45, 135, _____, _____, _____  0.5, 2, 8, 32, _____, _____, _____  -32, 16, -8, 4, _____, _____,

Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015.

Taylor Series & Error. Series and Iterative methods Any series ∑ x n can be turned into an iterative method by considering the sequence of partial sums.

Math 3120 Differential Equations with Boundary Value Problems

Simpson Rule For Integration.

SECOND-ORDER DIFFERENTIAL EQUATIONS Series Solutions SECOND-ORDER DIFFERENTIAL EQUATIONS In this section, we will learn how to solve: Certain.

76.8 – Average Rate of Change = = -9 = – Average Rate of Change = = -9 =

Copyright © Cengage Learning. All rights reserved. 17 Second-Order Differential Equations.

Differentiating exponential functions.

In Section 4.1, we used the linearization L(x) to approximate a function f (x) near a point x = a:Section 4.1 We refer to L(x) as a “first-order” approximation.

For any function f(x,y), the first partial derivatives are represented by f f — = fx and — = fy x y For example, if f(x,y) = log(x sin.

Copyright © Cengage Learning. All rights reserved Partial Derivatives.

Implicit Differentiation 3.6. Implicit Differentiation So far, all the equations and functions we looked at were all stated explicitly in terms of one.

Find the value of y such that

In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.

Polynomials. Polynomial a n x n + a n-1 x n-1 +….. + a 2 x 2 + a 1 x + a 0 Where all exponents are whole numbers – Non negative integers.

Higher order derivative patterns

Dr. Omar Al Jadaan Assistant Professor – Computer Science & Mathematics General Education Department Mathematics.

Sec 3.1: DERIVATIVES of Polynomial and Exponential Example: Constant function.

Section 4.5 Direct Variation. What happens to Y as X goes up by 1?

Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =

Properties of Functions. First derivative test. 1.Differentiate 2.Set derivative equal to zero 3.Use nature table to determine the behaviour of.

GRAPHING VERTICAL TRANSLATIONS OF PARABOLAS. Recall: Vertical Translations  When you add a constant to the end of the equation for a parabola, you translate.

5.6 Integration by Substitution Method (U-substitution) Thurs Dec 3 Do Now Find the derivative of.

What is a ZERO of a function? Morgan White Airline High School Algebra I Students, you should move on to the next slide in order to learn an introduction.

Derivation of the 2D Rotation Matrix Changing View from Global to Local X Y X’ Y’  P Y Sin  X Cos  X’ = X Cos  + Y Sin  Y Cos  X Sin  Y’ = Y Cos.

Starter Simplify (4a -2 b 3 ) -3. Polynomials Polynomial a n x n + a n-1 x n-1 +….. + a 2 x 2 + a 1 x + a 0 Where all exponents are whole numbers –

In this section, we will investigate how we can approximate any function with a polynomial.

Lesson 9-2 Factoring Using the Distributive Property.

Aim: How do we take second derivatives implicitly? Do Now: Find the slope or equation of the tangent line: 1)3x² - 4y² + y = 9 at (2,1) 2)2x – 5y² = -x.

Implicit Differentiation

10.4 Solving Factored Polynomial Equations

Solving Systems using Substitution

12.2 Finding Limits Algebraically

Differentiating Polynomials & Equations of Tangents & Normals

Higher-Order Linear Homogeneous & Autonomic Differential Equations with Constant Coefficients MAT 275.

Warmup Solve –2x2 + 5x = 0. Approximate non-integral answers. A. 0

Other Types of Equations

Algebraic Expressions and Identities by Siby Sebastian PGT(Maths)

Sec 3.1: DERIVATIVES of Polynomial and Exponential

Applications of the Derivative

Find all solutions of the polynomial equation by factoring and using the quadratic formula. x = 0 {image}

4-7 Sequences and Functions

Like Terms and Evaluating Expressions

Warm Up Simplify: a)

Sequences The values in the range are called the terms of the sequence. Domain: …....n Range: a1 a2 a3 a4….. an A sequence can be specified by.

Solving Systems of Equation by Substitution

Non-Calculator Questions

Part (a) Keep in mind that dy/dx is the SLOPE! We simply need to substitute x and y into the differential equation and represent each answer as a slope.

Copyright © Cengage Learning. All rights reserved.

Geometric Sequences and series

Legendre Polynomials Pn(x)

Indicator 16 System of Equations.

Classifying Polynomials

Presentation transcript:

Higher Order Derivatives

Find if. Substitute back into the equation.

Examples: 1.Find the 2 nd derivative of : y = 2.The 15 th derivative of a certain polynomial is a non-zero constant. What can you say about the polynomial? 3.Find the 2 nd derivative of : y = y 2 + xy = 4 4.Consider the fnc. y = 1/x. Take the first few derivatives and then find a nice way to represent the nth derivative. 5.Find the first 6 derivatives of y = cos x, then figure out what the 100 th derivative of y would be. 6.Compute the second derivative of y = (e x + e -x ) Compute the second derivative of f(x)=ln(x 2 +x).

More Examples: 1.Find the first 3 derivatives of y=5x 4 -3x 3 +7x 2 -9x+2 2.Find f (4) if y = 3.Find the first 6 derivatives of y = x 4 4.Find the first 3 derivatives of y = cos (x 2 )