Objectives Determine tangent lines to functions for a given point Compute the slope of curves Compute Instantaneous rate of change.

Slides:



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

Unit 6 – Fundamentals of Calculus Section 6
Sec 3.1: Tangents and the Derivative at a Point
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.
The derivative as the slope of the tangent line (at a point)
Chapter 2  2012 Pearson Education, Inc. Section 2.4 Rates of Change and Tangent Lines Limits and Continuity.
2 Derivatives.
2.4 Rates of Change and Tangent Lines. What you’ll learn about Average Rates of Change Tangent to a Curve Slope of a Curve Normal to a Curve Speed Revisited.
Warmup describe the interval(s) on which the function is continuous
Rate of change and tangent lines
Rates of Change and Tangent Lines
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 2.4 Rates of Change and Tangent Lines.
The Derivative Chapter 3:. What is a derivative? A mathematical tool for studying the rate at which one quantity changes relative to another.
Business Calculus Rates of Change Types of Change  Average rate of change: the average rate of change of y with respect to x is a ratio of.
THE DERIVATIVE AND THE TANGENT LINE PROBLEM
DO NOW: Use Composite of Continuous Functions THM to show f(x) is continuous.
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.
The Derivative. Objectives Students will be able to Use the “Newton’s Quotient and limits” process to calculate the derivative of a function. Determine.
1.4 – Differentiation Using Limits of Difference Quotients
2.4 Rates of Change and Tangent Lines
Determining Rates of Change from an Equation
RATES OF CHANGE & TANGENT LINES DAY 1 AP Calculus AB.
Find an equation of the tangent line to the curve at the point (2,3)
3.1 –Tangents and the Derivative at a Point
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 =
The Tangent and Velocity Problem © John Seims (2008)
Lesson 2-4 Tangent, Velocity and Rates of Change Revisited.
Section 2.6 Tangents, Velocities and Other Rates of Change AP Calculus September 18, 2009 Berkley High School, D2B2.
2.4 Rates of Change and Tangent Lines Calculus. Finding average rate of change.
Tangents. The slope of the secant line is given by The tangent line’s slope at point a is given by ax.
Chapter 3.1 Tangents and the Derivative at a Point.
December 3, 2012 Quiz and Rates of Change Do Now: Let’s go over your HW HW2.2d Pg. 117 #
§3.2 – The Derivative Function October 2, 2015.
Tangents, Velocities, and Other Rates of Change Definition The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope.
Review: 1) What is a tangent line? 2) What is a secant line? 3) What is a normal line?
AIM : How do we find tangent lines to a graph? Do Now: Find the slope of the line shown below that goes through points (0,6) and (3,0). HW2.1: p66-67 #9,10,19,22,23.
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.
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.
Section 2.1 – Average and Instantaneous Velocity.
§3.1 – Tangent Lines, Velocity, Rate of Change October 1, 2015.
Limits (10/14/11) Question: How can we compute the slope of the tangent line to the curve y = x 2 at the point (1, 1)? Possible approach: Compute the slope.
Section 1.4 The Tangent and Velocity Problems. WHAT IS A TANGENT LINE TO THE GRAPH OF A FUNCTION? A line l is said to be a tangent to a curve at a point.
Section 2.4 Rates of Change and Tangent Lines Calculus.
Rates of Change and Tangent Lines Devil’s Tower, Wyoming.
1 10 X 8/30/10 8/ XX X 3 Warm up p.45 #1, 3, 50 p.45 #1, 3, 50.
Average and Instantaneous Velocity. Average or Instantaneous? Instantaneous velocity : the velocity of a moving object at one specific moment. Average.
Ch. 2 – Limits and Continuity 2.4 – Rates of Change and Tangent Lines.
Calculus Section 3.1 Calculate the derivative of a function using the limit definition Recall: The slope of a line is given by the formula m = y 2 – y.
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).
2-4 Rates of change & tangent lines
2.1 Tangents & Velocities.
2.4 Rates of Change and Tangent Lines Day 1
2.1A Tangent Lines & Derivatives
Sec 2.7: Derivative and Rates of Change
2 Derivatives.
Tangent Lines & Rates of Change
Derivatives by Definition
THE DERIVATIVE AND THE TANGENT LINE PROBLEM
Tangent Lines and Derivatives
The Tangent and Velocity Problems
2.2C Derivative as a Rate of Change
Definition of a Derivative
2.7/2.8 Tangent Lines & Derivatives
Rates of Change and Tangent Lines
Section 2.1 – Average and Instantaneous Velocity
30 – Instantaneous Rate of Change No Calculator
The derivative as the slope of the tangent line
Sec 2.7: Derivative and Rates of Change
Linear approximation Median home prices in Austin
Presentation transcript:

Objectives Determine tangent lines to functions for a given point Compute the slope of curves Compute Instantaneous rate of change

Recall – Average Rate of Change

Definition – Secant Line A line through two points on a curve is a SECANT to the curve.

Slope of Secant Line

You Try

Observation What’s the association between average rate of change and the slope of the tangent line?

Flies/Day

Defn – Tangent Lines A line that intersects a function at exactly one point over a given interval.

How to find the slope of the tangent for a curve

Example – Slope of a tangent line

Secant Slope Calculation

Example – Slope of a tangent line

Important procedure

HW #8, Compute the slope of the secant lines and arrange them in ascending order. What are the appropriate units? 9 – 12 only (a) for these

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com. Inc. All rights reserved.