'Difference quotient' diaporamas de présentation

Derivative

Derivative. x. b - a. Average Rate of Change of f over [a, b]: Difference Quotient The average rate of change of the function f over the interval [a, b] is Average rate of change of f = f = f(b) - f(a) =Slope of line through points P and Q in the figure.

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Limits, Continuity and the Derivative

Limits, Continuity and the Derivative. The Derivative and the Slope of a Graph. Consider the case of an object moving along a curve from left to right. At the point where the object is released, it continues in a straight line. This line is called the tangent line .

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Section 2.1 The Derivative & the Tangent Line Problem

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Learning Objectives for Section 10.4 The Derivative

Learning Objectives for Section 10.4 The Derivative . The student will be able to calculate rate of change and slope of the tangent line. The student will be able to interpret the meaning of the derivative. The student will be able to identify the nonexistence of the derivative.

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Introduction to Functions and Graphs

1. Introduction to Functions and Graphs. 1.5 Functions and Their Rates of Change. Functions and Their Rates of Change. 1.5. Identify where a function is increasing or decreasing Use interval notation Use and interpret average rate of change Calculate the difference quotient.

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The Derivative

The Derivative. Recall : The slope of the tangent line to the graph of f(x) at any value of x can be found using limits and the difference quotient:.

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Aim: What do slope, tangent and the derivative have to do with each other?

Aim: What do slope, tangent and the derivative have to do with each other?. Do Now: What is the equation of the line tangent to the circle at point (7, 8)? . A secant of a circle is a line that intersects the circle in two points. Tangents & Secants.

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Velocity, Acceleration, Jerk

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5,000

x. 3. 0. t. 20. 5,000. 10,000. M. Time (min). 2. 4. -1. 1. 2. 3. 1. y.

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Economics 2301

Economics 2301. Lecture 17 Differential. Average and marginal functions. The average function rises as long as the marginal function lies above it. The average function declines as long as the marginal function lies below it. Average and marginal functions. Basic Question.

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Rates of Change

Rates of Change. Lesson 3.3. Rate of Change. Consider a table of ordered pairs (time, height). Using this data, how could we find the speed (in feet per second) of the sky diver?. Average Rate of Change. Recall formula for slope of a line through two points

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Welcome to another new day of:

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Learning Objectives for Section 10.6 Differentials

Learning Objectives for Section 10.6 Differentials. The student will be able to apply the concept of increments. The student will be able to compute differentials. The student will be able to calculate approximations using differentials. Increments.

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Equations of Lines

Equations of Lines . Chapter 1Seciton4. Forms for the Equation of a Line. Slope-Intercept form: m is the slope(rate of change) and b is the y-intercept (initial value when x = 0). Point-Slope form : m is the slope and is a known point. Example 2.

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2.6 Operations and Composition

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Lesson 3.7

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Pre calculus POD- Find the slope of each line containing the given points. Homework p.163 1-27 odds

Pre calculus POD- Find the slope of each line containing the given points. Homework p.163 1-27 odds. ( 3, 4) and ( 2, -1) ( -5, -2 ) and ( a, b) (x, f(x) ) and ( (x+h) , f(x+h) ). Difference Quotient. Find the difference quotient for.

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