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Unformatted text preview: Lecture 11 1 Lecture 11: The Derivative of a Function, Part II: (Sec. 2.6) Rates of Change, Differentiability Given a function y = f ( x ). The derivative of y with respect to x is the function f ′ defined by: f ′ ( x ) = Its domain: Lecture 11 2 The Slope of a Curve and the Derivative Def. The slope m of the graph of the curve y = f ( x ) at a given point ( x, f ( x )) is defined to be the slope of the tangent line to the curve at the point ( x, f ( x )) and is given by Lecture 11 3 The Derivative and Rates of Change ex. Let p ( x ) = 20 − . 02 x be the demand function for a product. 1) Find the revenue function R ( x ). 100 200 300 400 500 600 700 800 900 1000 1000 2000 3000 4000 5000 R ( x ) = 2) Use the graph to estimate the rate at which rev enue is changing when a) x = 100 b) x = 500 c) x = 900 Lecture 11 4 Consider again the revenue function R ( x ) = 20 x − . 02 x 2 and the following table of val ues: x 100 400 500 600 900 y 1800 4800 5000 4800 1800 1) What is the change in revenue as production in creases from 100 to 400 units?...
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 Spring '08
 Smith
 Calculus, Derivative, Slope, Velocity

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