Chapter1

# Chapter1 - Chapter 1 Functions...

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 1 of 115 Chapter 1 Functions

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 2 of 115 The Slope of a Straight Line The Slope of a Curve at a Point The Derivative Limits and the Derivative Differentiability and Continuity Some Rules for Differentiation More About Derivatives The Derivative as a Rate of Change Chapter Outline
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 3 of 115 § 1.1 The Slope of a Straight Line

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 4 of 115 Nonvertical Lines Positive and Negative Slopes of Lines Interpretation of a Graph Properties of the Slope of a Nonvertical Line Finding the Slope and y -Intercept of a Line Sketching the Graph of a Line Making Equations of Lines Slope as a Rate of Change Section Outline
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 5 of 115 Definition Example Equations of Nonvertical Lines : A nonvertical line L has an equation of the form The number m is called the slope of L and the point (0, b ) is called the y -intercept. The equation above is called the slope-intercept equation of L . For this line, m = 3 and b = -4. Nonvertical Lines . b mx y + = 4 3 - = x y

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 6 of 115 Lines – Positive Slope EXAMPLE EXAMPLE The following are graphs of equations of lines that have positive slopes.
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 7 of 115 Lines – Negative Slope EXAMPLE EXAMPLE The following are graphs of equations of lines that have negative slopes.

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 8 of 115 Interpretation of a Graph EXAMPLE EXAMPLE SOLUTION SOLUTION A salesperson’s weekly pay depends on the volume of sales. If she sells x units of goods, then her pay is y = 5 x + 60 dollars. Give an interpretation of the slope and the y -intercept of this straight line. First, let’s graph the line to help us understand the exercise. -40 60 160 260 360 460 -20 30 80 130 # of sales pay (80, 460)
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 9 of 115 Interpretation of a Graph The slope is 5, or 5/1. Since the numerator of this fraction represents the amount of change in her pay relative to the amount of change in her sales, the denominator, for every 1 sale that she makes, her pay increases by 5 dollars. The y -intercept is 60 and occurs on the graph at the point (0, 60). This point suggests that when she has executed 0 sales, her pay is 60 dollars. This \$60 could be referred to as her base pay . CONTINUED

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 10 of 115 Properties of the Slope of a Nonvertical Line
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 11 of 115 Properties of the Slope of a Line

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Goldstein/Schneider/Lay/Asmar,
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