Chapter 1.3 Lecture Notes
Chapter 1.3 Lecture Notes STAT 1102 - 003
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This 2 page Class Notes was uploaded by Kayla Notetaker on Saturday September 26, 2015. The Class Notes belongs to STAT 1102 - 003 at Temple University taught by Ron Kershner in Fall 2015. Since its upload, it has received 44 views. For similar materials see QUANTITATIVE METHODS FOR BUSINESS II in Statistics at Temple University.
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Date Created: 09/26/15
C13 Average of Change and Limits of Difference Quotients Review The slope between two points is the average rate of change 3392y1 fx2 fx1 IS the average rate of change formula x2 x1 x2x1 Remember fx is just another way to write y Difference Quotient The difference quotient is the slope of a secant line To find the slope of a secant line let X2 x h why do we do this h the distance between x1 and x2 x h x1 the distance between x1 and x2sss and let x1 x quot Plug into the slope formula fxhfx xh x The x s in the bottom cancel fxh fx h This is the formula for finding the slope of a secant line So what is a Secant line A secant line is a line that intersects the graph at TWO points Tangent line A tangent line is a line that TOUCHES the graph at ONE point So how do we find the slope of a tangent line Using the difference quotient we set the limit to 0 so when the distance between x1 and x2 is as close to nothing as possible forcing the secant line into a tangent Using the Difference Quotient Fx x2 Find difference quotient slope of secant line Plug in 1 fxhfx 39 h hf x2 h Foil x h x22xh hz x2 h Simplify th h2 h Pull out an H h2x h h H s cancel with each other leaving 2xh Find the difference quotient as h 0 slope of tangent line 1 We already found the quotient 2x h 2 Now set the limit h gt0 h Plug in rule sub 0 for h 2x O 2x is the limit
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