Explicit vs Implicit. Explicit: Explicit: A function defined in terms of one variable. y= 3x + 2 is defined in terms of x only. Implicit: Implicit: A.

Slides:

Advertisements

Similar presentations

Related Rates Finding the rates of change of two or more related variables that are changing with respect to time.

Advertisements

Solving Systems of Equations using Substitution

Lesson 12.1 Inverse Variation pg. 642

8-2: Solving Systems of Equations using Substitution

BALANCING 2 AIM: To solve equations with variables on both sides.

3.3 Solving equations with variables on both sides.

Solving Absolute Value Equations Solving Absolute Value Equations

U1B L2 Reviewing Linear Functions

2.4 – Solving Equations with the Variable on Each Side.

Use addition to eliminate a variable

Implicit Differentiation

Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.

2.5 Implicit Differentiation. Implicit and Explicit Functions Explicit FunctionImplicit Function But what if you have a function like this…. To differentiate:

Solving Systems of three equations with three variables Using substitution or elimination.

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

Elimination Day 2. When the two equations don’t have an opposite, what do you have to do? 1.

7.3 Solving Systems of Equations by Elimination (Addition & Subtraction) Solve by Elimination Example Problems Practice Problems.

3.5 – Solving Systems of Equations in Three Variables.

Implicit Differentiation

Implicit Differentiation

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

Example: Sec 3.7: Implicit Differentiation. Example: In some cases it is possible to solve such an equation for as an explicit function In many cases.

Calculus: IMPLICIT DIFFERENTIATION Section 4.5. Explicit vs. Implicit y is written explicitly as a function of x when y is isolated on one side of the.

Warm Up 10/3/13 1) The graph of the derivative of f, f ’, is given. Which of the following statements is true about f? (A) f is decreasing for -1 < x

Ms. Battaglia AB/BC Calculus. Up to this point, most functions have been expressed in explicit form. Ex: y=3x 2 – 5 The variable y is explicitly written.

Homework questions? 2-5: Implicit Differentiation ©2002 Roy L. Gover ( Objectives: Define implicit and explicit functions Learn.

Objectives: 1.Be able to determine if an equation is in explicit form or implicit form. 2.Be able to find the slope of graph using implicit differentiation.

Warm-Up: Find f’(x) if f(x)=(3x 2 -6x+2) 3. SECTION 6.4: IMPLICIT DIFFERENTIATION Objective: Students will be able to…  Take the derivative of implicitly.

Solving Linear Systems by Substitution O Chapter 7 Section 2.

Implicit Differentiation Objective: To find derivatives of functions that we cannot solve for y.

Implicit Differentiation. Implicitly vs. Explicitly Defined Functions y is given explicitly as a function of x (y is solved in terms of x) y is given.

3.7 – Implicit Differentiation An Implicit function is one where the variable “y” can not be easily solved for in terms of only “x”. Examples:

7.4. 5x + 2y = 16 5x + 2y = 16 3x – 4y = 20 3x – 4y = 20 In this linear system neither variable can be eliminated by adding the equations. In this linear.

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 =

7.3 Solving Systems of Equations by Elimination Using Multiplication Solve by Elimination Example Problems Practice Problems.

6.5: RELATED RATES OBJECTIVE: TO USE IMPLICIT DIFFERENTIATION TO RELATE THE RATES IN WHICH 2 THINGS ARE CHANGING, BOTH WITH RESPECT TO TIME.

Solving Multi-Step Equations Using Inverse Operations.

DO NOW: Find the inverse of: How do you find the equation of a tangent line? How do you find points where the tangent line is horizontal?

Warm-up. Systems of Equations: Substitution Solving by Substitution 1)Solve one of the equations for a variable. 2)Substitute the expression from step.

Aim: Finding the slope of the tangent line using implicit differentiation Do Now: Find the derivative 1)y³ + y² - 5y – x² = -4 2) y = cos (xy) 3) √xy =

FIRST DERIVATIVES OF IMPLICIT FUNCTIONS

Implicit Differentiation

Section 3.7 Implicit Functions

Implicit Differentiation

Solving Systems using Substitution

Implicit Differentiation

Developing approaches to learning skills Step 1Objective strand: Approaches to learning skill: Step 2Explicit learning experience: Step 3Implicit learning.

3-2: Solving Systems of Equations using Substitution

6-2 Solving Systems By Using Substitution

1.4 Rewrite Formulas and Equations

Implicit Differentiation

3-2: Solving Systems of Equations using Substitution

Solving Systems of Equations using Substitution

Implicit Differentiation

3-2: Solving Systems of Equations using Substitution

Who Wants to be an Equationaire?. Who Wants to be an Equationaire?

Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Use power series to solve the differential equation. y ' = 7xy

Warm Up 12/3/2018 Solve by substitution.

TWO STEP EQUATIONS 1. SOLVE FOR X 2. DO THE ADDITION STEP FIRST

3-2: Solving Systems of Equations using Substitution

Implicit Differentiation & Related Rates

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

Equations With Two Variables pages

Presentation transcript:

Explicit vs Implicit

Explicit: Explicit: A function defined in terms of one variable. y= 3x + 2 is defined in terms of x only. Implicit: Implicit: A function defined in terms of two or more variables. y 2 + 2xy + 3x 2 = 12 is defined in terms of x and y. You can’t solve the equation for either x or y only.

Identify each function as either explicit or implicit. Polling question: 1.2

Find the derivative of the explicit functions Page 1.3 Page 1.4 Page 1.5

Find the derivative of the implicit functions Student practice page 1.6 Student practice page 1.7 Student practice page 1.8

Student practice page 1.9

Student practice page 1.10