Tangent Lines and Derivatives. Definition of a Tangent Line The tangent line to the curve y=f(x) at the point P(a,f(a)) is the line through P with slope.

Slides:

Advertisements

Similar presentations

2.7 Tangents, Velocities, & Rates of Change

Advertisements

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.

Equations of Tangent Lines

3.1.Tangent Lines and Rates of Change. Average and instantenious velocity. Rita Korsunsky.

Copyright © 2011 Pearson Education, Inc. Slide Tangent Lines and Derivatives A tangent line just touches a curve at a single point, without.

Tangent lines Recall: tangent line is the limit of secant line The tangent line to the curve y=f(x) at the point P(a,f(a)) is the line through P with slope.

The Derivative Chapter 3:. What is a derivative? A mathematical tool for studying the rate at which one quantity changes relative to another.

 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.

DO NOW: Use Composite of Continuous Functions THM to show f(x) is continuous.

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.

CHAPTER Continuity Derivatives Definition The derivative of a function f at a number a denoted by f’(a), is f’(a) = lim h  0 ( f(a + h) – f(a))

2-2: Differentiation Rules Objectives: Learn basic differentiation rules Explore relationship between derivatives and rates of change © 2002 Roy L. Gover.

3.1 –Tangents and the Derivative at a Point

Lesson 2-4 Tangent, Velocity and Rates of Change Revisited.

Chapter 3: Derivatives 3.1 Derivatives and Rate of Change.

Section 2.6 Tangents, Velocities and Other Rates of Change AP Calculus September 18, 2009 Berkley High School, D2B2.

3.1 Derivatives and Rates of Change 12.7 Derivatives and Rates of Change.

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

Tangents. The slope of the secant line is given by The tangent line’s slope at point a is given by ax.

Math 1304 Calculus I 2.7 – Derivatives, Tangents, and Rates.

Basic Differentiation Rules

Basic Differentiation Rules and Rates of Change Section 2.2.

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.

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.

TANGENT LINES Notes 2.4 – Rates of Change. I. Average Rate of Change A.) Def.- The average rate of change of f(x) on the interval [a, b] is.

Derivative Notation and Velocity. Notation for the Derivative.

Rate of Change. What is it? A slope is the rate at which the y changes as the x changes Velocity is the rate the position of an object changes as time.

Business Calculus Derivative Definition. 1.4 The Derivative The mathematical name of the formula is the derivative of f with respect to x. This is the.

Calc Tangents, Velocities and Other Rates of Change Looking to calculate the slope of a tangent line to a curve at a particular point. Use formulas.

Acceleration and Deceleration Section 7.4. Acceleration Acceleration is the rate of change of the rate of change. In other words, acceleration = f’’(x)

Warm - up 1) Enter the data into L1 and L2 and calculate a quadratic regression equation (STAT  calc Quadreg). Remember: time – x distance – y. 2) Find.

2.2 Basic Differentiation Rules and Rate of Change

Section 12-3 Tangent Lines and velocity (day2)

2.1 Tangents & Velocities.

12.3 Tangent Lines and Velocity

Activity 5-2: Understanding Rates of Change

Rate of Change.

2.1A Tangent Lines & Derivatives

2.7 Derivatives and Rates of Change

Rate of change and tangent lines

Instantaneous Rates Instantaneous rates are still connected to the concept of the tangent line at some point. However, we will be getting an algebraic.

Calculus I (MAT 145) Dr. Day Monday September 25, 2017

Sec 2.7: Derivative and Rates of Change

The Derivative and the Tangent Line Problems

Derivatives by Definition

Derivatives Created by Educational Technology Network

Lesson 7: Applications of the Derivative

Lesson 7: Applications of the Derivative

Tangent Lines and Derivatives

The Tangent and Velocity Problems

Today’s Learning Goals …

Click to see each answer.

Prep Book Chapter 5 – Definition of the Derivative

2.7/2.8 Tangent Lines & Derivatives

Packet #4 Definition of the Derivative

Prep Book Chapter 5 – Definition pf the Derivative

Unit 3 Functions.

2.2: Formal Definition of the Derivative

30 – Instantaneous Rate of Change No Calculator

Introduction to Calculus

Section 2.2 Day 2 Basic Differentiation Rules & Rates of Change

Calculus 3-4 Rates of Change.

Click to see each answer.

Presentation transcript:

Tangent Lines and Derivatives

Definition of a Tangent Line The tangent line to the curve y=f(x) at the point P(a,f(a)) is the line through P with slope

Finding a Tangent Line to a Hyperbola Find an equation of the tangent line at the point (3,1).

Another way to find slope of a tangent line

Finding a Tangent Line Find an equation of the tangent line to the curve at the point (1,2).

Definition of a Derivative The derivative of a function is the slope of the tangent line…so….

Finding a Derivative at a Point Find the derivative of the function at the number 2.

Finding a Derivative Find f’(a), f’(1), f’(4), and f’(9).

Instantaneous Rate of Change

Instantaneous Velocity of a Falling Object If an object is dropped from a height of 3000 ft, its distance above the ground (in feet) after t seconds is given by h(t). Find the object’s instantaneous velocity after 4 seconds.