Warm Up Determine for y2 + xy + 3x = 9.

Slides:

Advertisements

Similar presentations

Unit 6 – Fundamentals of Calculus Section 6

Advertisements

Remember: Derivative=Slope of the Tangent Line.

Equations of Tangent Lines

Equation of a Tangent Line

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

Calculus 2413 Ch 3 Section 1 Slope, Tangent Lines, and Derivatives.

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

Derivative Review Part 1 3.3,3.5,3.6,3.8,3.9. Find the derivative of the function p. 181 #1.

DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.

Meanings of the Derivatives. I. The Derivative at the Point as the Slope of the Tangent to the Graph of the Function at the Point.

 Find an equation of the tangent line to the curve at the point (2, 1).

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.

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

 Graph the following two lines:  1.  2.  Write an equation of the line that passes through (-3,3) and is parallel to the line y=-2x+1.

Find an equation of the tangent line to the curve at the point (2,3)

x y no x y yes.

Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.

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

Differentiation. f(x) = x 3 + 2x 2 – 3x + 5 f’(x) = 3x 2 + 4x - 3 f’(1) = 3 x x 1 – 3 = – 3 = 4 If f(x) = x 3 + 2x 2 –

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

1 Implicit Differentiation. 2 Introduction Consider an equation involving both x and y: This equation implicitly defines a function in x It could be defined.

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

15. Implicit Differentiation Objectives: Refs: B&Z Learn some new techniques 2.Examples 3.An application.

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.

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.

1.6 – Tangent Lines and Slopes Slope of Secant Line Slope of Tangent Line Equation of Tangent Line Equation of Normal Line Slope of Tangent =

GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative.

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.

Solve and show work! State Standard – 4.1 Students demonstrate an understanding of the derivative of a function as the slope of the tangent line.

2.1 The Derivative and The Tangent Line Problem Slope of a Tangent Line.

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

5-5 WRITING THE EQUATION OF THE LINE MISS BATTAGLIA – GEOMETRY CP OBJECTIVE: WRITE AN EQUATION GIVEN THE SLOPE OF A POINT; WRITE AN EQUATION GIVEN TWO.

Today in Calculus Derivatives Graphing Go over test Homework.

Chapter 9 & 10 Differentiation Learning objectives: 123 DateEvidenceDateEvidenceDateEvidence Understand the term ‘derivative’ and how you can find gradients.

What happens if we graph a system of equations and the lines intersect? y = x-1 y = 2x-2.

Section 14.3 Local Linearity and the Differential.

Unit 2 Lesson #3 Tangent Line Problems

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

Rates of Change and Tangent Lines

Warm Up a) What is the average rate of change from x = -2 to x = 2? b) What is the average rate of change over the interval [1, 4]? c) Approximate y’(2).

Implicit Differentiation

2-4 Rates of change & tangent lines

TANGENT LINE/ NORMAL LINE

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

2.1A Tangent Lines & Derivatives

TANGENT LINE/ NORMAL LINE

The Derivative and the Tangent Line Problems

Point-Slope Form Slope-Intercept Form

2-4: Tangent Line Review &

Warm Up Find the x and y intercept of the graph of 3x+4y=2

Implicit Differentiation

Calculus Implicit Differentiation

Solutions to Systems of Equations

(This is the slope of our tangent line…)

Unit 4: curve sketching.

Differentiate. f (x) = x 3e x

Tangent line to a curve Definition: line that passes through a given point and has a slope that is the same as the.

2.7/2.8 Tangent Lines & Derivatives

Write the equation for the following slope and y-intercept:

3. Differentiation Rules

5-4 point-slope form.

Objectives: To graph lines using the slope-intercept equation

3. Differentiation Rules

More with Rules for Differentiation

Warm up 21 1.) Determine the slope and y intercept of the line y=7x ) Determine the slope and the yintercept of the line 7x- 4y=3 3.) Graph y=1/2.

WARM UP Find the equation of the line that passes through (3, 4), (6,8)? Find the slope of the line that passes through (-4,-8), (12,16)? Find the equation.

Presentation transcript:

Warm Up Determine for y2 + xy + 3x = 9

Determine y’ for the equation:

Let y3x + y2x2 = 6 Confirm that the point (2,1) is a point on the curve. Find the slope of the curve at the point (2,1). Is the graph increasing or decreasing at that point? Explain. Write an equation of the tangent line to the curve at the point (2,1) Write an equation of the normal line to the curve at the point (2,1)

The second derivative is written Example: Determine for y2 + x2 = 25 Your Turn  x2 – y2 = 9