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Unformatted text preview: Lecture 21 — Tangent Line Approximations When a function is linear, we can predict its value at any point, since its rate of change is constant: Suppose the price p of a gallon of gasoline is $ 3 , and is decreasing 4 cents per day. What will be the price of gasoline in 1 day? 5 days? Write p as a function of time t in days. When it is not linear, we often try to “linearize” the function to approximate the values nearby: Suppose the price p of a gallon of gasoline is $ 3 , and it decreased by 4 cents TODAY. What is your best guess at the price of gasoline in 1 day? 5 days? Here we used our knowledge of the slope (rate of change) and the value of the function p to imagine it as a straight line— that is, we found the tangent line— to approximate the nearby values of p . Thus, the tangent line to the graph of f ( x ) at x = a is also called the linearization of f at a , and is written: The linearization at x = a : (1) (2) Find the linearization of the function f ( x ) = 3 √ x at...
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This note was uploaded on 05/27/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus, Approximation, Rate Of Change

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