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 =

Slides:

Advertisements

Similar presentations

Warm up Problems After correcting the homework, we will be taking Derivative Quiz #2.

Advertisements

Equations of Tangent Lines

Equations of Tangent Lines

Find the slope of the tangent line to the graph of f at the point ( - 1, 10 ). f ( x ) = 6 - 4x

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

Derivatives - Equation of the Tangent Line Now that we can find the slope of the tangent line of a function at a given point, we need to find the equation.

3.5 Lines in the Coordinate Plane

Finding the Equation of a Line Critical Thinking Skill: Explicitly assess information and draw conclusions.

Summer Assignment Review

5.4 Point Slope Form.

Graphing Linear Equations. Identifying a Linear Equation A linear equation is any equation that can be put in the form... Ax + By = C... where A, B, and.

Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.

The point-slope form of a linear equation of a non- vertical line is given by: Point-Slope Form of a Linear Equation.

5.4 Point-Slope Form of a Linear Equation

2.4 Chain Rule. Chain Rule If y=f(u) is a differentiable function of u and u=g(x) is a differentiable function of x then y=f(g(x)) is a differentiable.

TODAY IN ALGEBRA… Warm up: 5.2 Review-Writing an equation of a line given two points Learning Goal: 5.3 Writing a linear equation in Point-Slope form.

Warm-Up Find the slope of the line that passes through the two points:

Section 6.1: Euler’s Method. Local Linearity and Differential Equations Slope at (2,0): Tangent line at (2,0): Not a good approximation. Consider smaller.

TODAY IN ALGEBRA…  Warm up: Calculating Slope  Learning Goal: 5.1b You will write equations of lines in slope intercept form given two points  Independent.

2-4: Writing Linear Equations Using Slope Intercept Form.

Lesson 5.6 Point-Slope Form of the Equation of a Line.

Section 2.4 Notes: Writing Linear Equations. Example 1: Write an equation in slope-intercept form for the line.

Mrs. Rivas International Studies Charter School.Objectives: slopes and equations 1.Find slopes and equations of tangent lines. derivative of a function.

ALGEBRA 1 Lesson 5-4 Warm-Up. ALGEBRA 1 “Point-Slope Form and Writing Linear Equations” (5-4) (5-3) What is “point- slope form”? How can you use point-slope.

Lesson 2.7 AIM: How to find the slope and equation of a line using two points.

Slope The slope of a linear equation is the same everywhere along the line. We know how to use slope-intercept form: In slope-intercept form, the slope.

6.5 Point – Slope Form. Quick Review 1. What is the Slope-Intercept Form? y = mx + b 2. What is the Standard Form? Ax + By = C 3. How does an equation.

5.2 Point slope form Obj: I can use point slope form to write the equation of a line. Write down HW Test corrections are due Thursday. I will be out again.

Graphing Test Review Algebra.

Chapter 5, What Linear Equations are all about Winter, (brrrr…)

5-2B Two-Point Equation of a Line Warm-up (IN) Learning Objective: to determine the equation of a line through 2 given points. Rewrite the equations in.

Warm up Problems Implicit Differentiation Ex. So far, all problems have been y = f (x)  What if x’s and y’s are mixed together?

Point slope form of an equation Y - y₁ = m(X- x₁) (x₁, y₁) An ordered pair on the line m slope.

Point slope form of an equation Y - y₁ = m(X- x₁) (x₁, y₁) An ordered pair on the line m slope.

TODAY IN ALGEBRA…  Warm up: Writing an equation of a line given two points  Learning Goal: 5.2 You will write an equation of a line in slope-intercept.

Geo A Chapter 7 Writing Linear Equations Write the point-slope form of the line that passes through the point (-3, -1) and has a slope of 1.

6.4 Point-Slope Form and Writing Linear Equations Point-Slope Form of a Linear Equation –The point-slope form of the equation of a non- vertical line that.

Algebra I Section 4-3 Point-Slope Form. Point - Slope Form y - y 1 = m (x - x 1 ) m = slope ( x 1, y 1 ) -- ordered pair.

Section 6-: Point-slope Form of a Linear Equation SPI 22C: select the graph that represents a given linear function Objective: Graph and write linear equations.

5.5 Writing Equations in Point-Slope Form

Sec. 3.3: Rules of Differentiation. The following rules allow you to find derivatives without the direct use of the limit definition. The Constant Rule.

Use point-slope form to write an equation EXAMPLE 3 Write an equation in point-slope form of the line shown.

You can do it!!! 2.5 Implicit Differentiation. How would you find the derivative in the equation x 2 – 2y 3 + 4y = 2 where it is very difficult to express.

Lesson 3-7: Parallel & Perpendicular Lines Objectives Students will: Use equations to determine if two lines are parallel or perpendicular Write an equation.

More with Rules for Differentiation Warm-Up: Find the derivative of f(x) = 3x 2 – 4x 4 +1.

Warm Up. Equations of Tangent Lines September 10 th, 2015.

Aim: What is the equation of a line? Do Now: Find the slope of the line 8x + 5y = 20 This is the slope – intercept form y = mx + b HW: Handout.

2.6 Finding equations of lines. Review Slope-Intercept Form: y = mx + b Point-Slope Form: y – y 1 = m (x – x 1 )

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?

Algebra 1 Foundations, pg 338  Students will be able to write and graph linear equations using point-slope form.

5-4 Point-Slope Form and Writing Linear Equations Hubarth Algebra.

Objective - To write equations given the slope and a point using Point-Slope Form. Point-Slope Form Write the equation of a line in point-slope form that.

Linear Equations & Point-Slope Form. Point Slope Form/Equation Builder BACK.

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.

0-6 Writing Equations in Point- Slope Form. Slope Formula y 1 – y 2 x 1 – x 2 Forms of lines Point-slope form: y – y 1 = m (x - x 1 )

 Slope-Intercept Form:  y = mx + b  where m is the slope and b is the y-intercept.  How do you know you have b? Either you will see b = ??, or you.

Aim: How do we find points of intersection? What is slope? Do Now: Is the function odd, even or neither? 1)y - x² = 7 2)y = 6x - x⁷ 3)y = √ x⁴ - x⁶ 4)Find.

TANGENT LINE/ NORMAL LINE

Used for composite functions

Find the equation of the tangent line for y = x2 + 6 at x = 3

TANGENT LINE/ NORMAL LINE

MTH1170 Implicit Differentiation

2.5 Implicit Differentiation

Implicit Differentiation

Implicit Differentiation

Implicit Differentiation

Implicit Differentiation & Related Rates

7. Implicit Differentiation

More with Rules for Differentiation

Point-Slope Form y – y1 = m(x – x1)

Presentation transcript:

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 = x – 2y HW #23 – pg 139 #17,19,21,24,25

Finding the slope of the tangent line implicitly 1)Find the derivative implicitly 2)Plug in the values for x and y to find the slope. Example: Find the slope of the tangent line for x² + 4y² = 4 at (√2, -1/√2)

Other Examples: 1)x² - y³ = 0 at (1,1) 2)(x + y)³ = x³ + y³ at (-1,1)

To find the equation of the tangent line: Find the (derivative)slope – use the slope and the coordinate pair to find the equation – either point-slope or slope-intercept form. Find the equation of the tangent line: 1) x² + y² = 20 at (2,4)

Try these: 1)x² - y² = 16 at (5,3) 2)3(x² + y²)² = 100xy at (3,1)