Find the equation of the tangent line to the curve y = 1 / x that is parallel to the secant line which runs through the points on the curve with x - coordinates.

Slides:



Advertisements
Similar presentations
2.7 Tangents, Velocities, & Rates of Change
Advertisements

Unit 6 – Fundamentals of Calculus Section 6
Remember: Derivative=Slope of the Tangent Line.
Tangent Lines ( Sections 1.4 and 2.1 ) Alex Karassev.
2.1 Derivatives and Rates of Change. The slope of a line is given by: The slope of the tangent to f(x)=x 2 at (1,1) can be approximated by the slope of.
Slope and Equation of a line How to find the slop of a line? (x 1, y 1 ) (x 2, y 2 ) How to find the equation of a line? Sec 2.1: Rates of Change and.
Equation of a Tangent Line
Introduction to Differentiation Motion Graphs. Travel Graph Describe what is happening at each stage of this travel graph
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.
Rates of Change and Tangent Lines
Point Value : 20 Time limit : 2 min #1 Find. #1 Point Value : 30 Time limit : 2.5 min #2 Find.
12: Tangents and Gradients © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules.
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.
THE DERIVATIVE AND THE TANGENT LINE PROBLEM
AB 11 22 33 44 55 66 77 88 99 10  20  19  18  17  16  15  14  13  12  11  21  22  23  24  25  26  27  28.
Geometry – Segments of Chords and Secants
Rates of Change and Tangent Lines Section 2.4. Average Rates of Change The average rate of change of a quantity over a period of time is the amount of.
10.5: Find Segment Lengths in Circles
Equations of Lines; Building Linear Functions January 22, 2007.
1.4 – Differentiation Using Limits of Difference Quotients
Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.
1 Lesson 10.6 Segment Formulas. 2 Intersecting Chords Theorem A B C D E Interior segments are formed by two intersecting chords. If two chords intersect.
Equations of Tangent Lines April 21 st & 22nd. Tangents to Curves.
Find an equation of the tangent line to the curve at the point (2,3)
AP Calculus/Cal culus 2A, 2B. Think – Pair – Group Share – Whole class Share.
Mrs. Rivas International Studies Charter School.Objectives: slopes and equations 1.Find slopes and equations of tangent lines. derivative of a function.
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 =
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.
Tangents. The slope of the secant line is given by The tangent line’s slope at point a is given by ax.
Warm Up Determine a) ∞ b) 0 c) ½ d) 3/10 e) – Rates of Change and Tangent Lines.
2.1 The Derivative and The Tangent Line Problem Slope of a Tangent Line.
UNIT 1B LESSON 7 USING LIMITS TO FIND TANGENTS 1.
OBJECTIVES: To introduce the ideas of average and instantaneous rates of change, and show that they are closely related to the slope of a curve at a point.
If f (x) is continuous over [ a, b ] and differentiable in (a,b), then at some point, c, between a and b : Mean Value Theorem for Derivatives.
Chapter 9 & 10 Differentiation Learning objectives: 123 DateEvidenceDateEvidenceDateEvidence Understand the term ‘derivative’ and how you can find gradients.

Section 3.2 Mean Value Theorem Math 1231: Single-Variable Calculus.
6.7 Graphing Other Trigonometric Functions Objective: Graph tangent, cotangent, secant, and cosecant functions. Write equations of trigonometric functions.
Unit 2 Lesson #3 Tangent Line Problems
2-4 Rates of change & tangent lines
2.1 Tangents & Velocities.
Tangent Lines (Sections 2.1 and 3.1 )
2.4 Rates of Change and Tangent Lines Day 1
2.1A Tangent Lines & Derivatives
Equations and Inequalities involving Absolute Value
3.1 Polynomial & Exponential Derivatives
Equations of Tangents.
Differentiating Polynomials & Equations of Tangents & Normals
Find the derivative of the vector function r(t) = {image}
Differentiate the function. {image}
9-6 Other Angles.
Tangent Lines & Rates of Change
Solve the equation for x. {image}
Derivatives by Definition
THE DERIVATIVE AND THE TANGENT LINE PROBLEM
x = 4y - 4 x = 4y + 4 x = 4y - 1 y = 4x - 4 y = 4x - 1 y = 4x + 4
Differentiate. f (x) = x 3e x
a + 2 = 6 What does this represent? 2 a
Find {image} by implicit differentiation:    {image} .
30 – Instantaneous Rate of Change No Calculator
Do-Now Find the area of an equilateral triangle with side lengths of 26 ft. Reflect the point (3, –9) in the line y = x and state the coordinates of the.
Equation Review.
Special Segments in a Circle
Special Segments in a Circle
Gradients and Tangents
If {image} choose the graph of f'(x).
Section 9-6: Other Angles
Geometry/Trig 2 Name __________________________
Discovering the Chain Rule
Presentation transcript:

Find the equation of the tangent line to the curve y = 1 / x that is parallel to the secant line which runs through the points on the curve with x - coordinates equal 1 and 1.5. {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the right part of the equality. {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the right part of the equality Find the right part of the equality. If x and y are real numbers and a > 0, then a x + y = _____ a x / a y a x + y a x + a y a x a y 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the right part of the equality Find the right part of the equality. If x is real number and a, b > 0, then (ab) x = _____ a x + b x a b x a x / b x a x b x 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50