Instantaneous Rates & Concept of Derivative

Slides:



Advertisements
Similar presentations
Unit 6 – Fundamentals of Calculus Section 6
Advertisements

Sec 3.1: Tangents and the Derivative at a Point
Welcome To Calculus (Do not be afraid, for I am with you) The slope of a tangent line By: Mr. Kretz.
Copyright © 2011 Pearson Education, Inc. Slide Tangent Lines and Derivatives A tangent line just touches a curve at a single point, without.
DERIVATIVES 3. DERIVATIVES In this chapter, we begin our study of differential calculus.  This is concerned with how one quantity changes in relation.
Rate of change and tangent lines
The Derivative Eric Hoffman Calculus PLHS Sept
The Derivative Chapter 3:. What is a derivative? A mathematical tool for studying the rate at which one quantity changes relative to another.
Differentiation The original function is the y- function – use it to find y values when you are given x Differentiate to find the derivative function or.
Who has the Power? Today you will investigate the slope of polynomial Parent Graphs and infer an important rule.
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.
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.
1 of 30 1 st Derivative The formula for the 1 st derivative of a function is as follows: It’s just the difference between subsequent values and measures.
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.
Measuring the length and distance
Equations of Tangent Lines April 21 st & 22nd. Tangents to Curves.
Chapter Acceleration Non-uniform motion – more complex.
Calendar Mon., 12/8 Topic: Velocity-Time Graphs Homework: Finish any incomplete work between pg. 95 & 103 To Do Pick up 2 papers from the Pick Up table.
MAT 125 – Applied Calculus 3.2 – The Product and Quotient Rules.
The derivative of a function f at a fixed number a is In this lesson we let the number a vary. If we replace a in the equation by a variable x, we get.
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.
Chapter 3.1 Tangents and the Derivative at a Point.
Lesson 51 – Derivatives As Functions IB Math SL1 - Santowski 12/9/2015 Math SL1 - Santowski 1.
December 3, 2012 Quiz and Rates of Change Do Now: Let’s go over your HW HW2.2d Pg. 117 #
MAT 125 – Applied Calculus 3.3 – The Chain Rule Today’s Class  We will be learning the following concepts today:  The Chain Rule  The Chain Rule for.
5.3:Higher Order Derivatives, Concavity and the 2 nd Derivative Test Objectives: To find Higher Order Derivatives To use the second derivative to test.
Take out a paper and pencil (and eraser) It is now your turn.
Warm Up. Equations of Tangent Lines September 10 th, 2015.
Today in Calculus Derivatives Graphing Go over test Homework.
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.
Rates of Change and Tangent Lines Devil’s Tower, Wyoming.
Warm-Up: Factor by GCF 1. 16x 2 – 8x 2. 10x – 10y.
You have 10 seconds to name…
It’s ‘review for the test’ day. But first, we have to finish the dilations section.
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.
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.
Using the Graphing Calculator to Find Area Under a Curve
3-3 rules for differentiation
Warm Up Determine for y2 + xy + 3x = 9.
2.1 Tangents & Velocities.
Section 11.3A Introduction to Derivatives
2.1A Tangent Lines & Derivatives
Rate of change and tangent lines
Derivative Rules 3.3.
3.1 Polynomial & Exponential Derivatives
Instantaneous Rates Instantaneous rates are still connected to the concept of the tangent line at some point. However, we will be getting an algebraic.
Sec 2.7: Derivative and Rates of Change
Interior Angles of Triangles
Definition of the Derivative
2-4: Tangent Line Review &
Evaluating Text What do you think?.
The Derivative as a Function
Concavity and the Second Derivative Test
#1. | | # Simplify the expressions using the Distributive Property #3. 2 ( 1 + 5) #4. 3 ( y + 5 ) Bell Ringer.
2.2C Derivative as a Rate of Change
Differentiate. f (x) = x 3e x
2.4 cosine law Let’s take a look at various trigonometric curves before moving on Understanding how the curves look for sine, cosine, tangent and their.
Section 3.2 Calculus AP/Dual, Revised ©2017
2.7/2.8 Tangent Lines & Derivatives
32 – Applications of the Derivative No Calculator
Differentiation Summary
30 – Instantaneous Rate of Change No Calculator
20A, 20B Rate of Change, 20C The Derivative Function
This and These.
35 – Local Linearization No Calculator
Instantaneous Speed Science 1206.
#1. | | # Simplify the expressions using the Distributive Property #3. 2 ( 1 + 5) #4. 3 ( y + 5 ) Bell Ringer.
Instantaneous Speed 10.7.
Wow, THAT is one big, big, big question. Here’s a curve.
Presentation transcript:

Instantaneous Rates & Concept of Derivative 7.1 - Concept of the derivative as a rate of change Tangent to a curve

1st Complete Handout in Partners You need to get in partners and complete the worksheet: “Learning Activity 2.3 – Instantaneous Rates of Change” You will need: Pencil Calculator Straight-edge or ruler

2nd Complete “Investigation #3” Next, turn to pg. 566 in your ORANGE BOOK and complete “Investigation 3” Only complete questions 1 – 3 Both of these activities should be completed by the middle of the 2nd period Let me know if you have any questions