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ws27 - WORKSHEET 27 Fall 1995 1 Below the graph of f(x = x2...

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WORKSHEET 27 - Fall 1995 1. Below, the graph of f ( x ) = x 2 is given. The line below the graph is the tangent line at x = 1. The lines above the graph connect the points (0 , 0), (1 , 1), and (2 , 4). 1 2 3 4 1 2 a) Find the area bounded by the tangent line, the x -axis, and the line x = 2. b) Find the area bounded by the two segments above the graph, the x -axis, and the line x = 0. the graph. c) Use your answers to a) and b) to venture a guess as to the area between the graph of f and the x -axis lying over the interval [0 , 2]. d) Find a function g such that g = f . What is g (2) g (0)? How close is this to your guess in part c)? Creepy, eh? There are several functions having x 2 as a derivative. What if you had chosen another? 2. Let f be a continuous function with f ( x ) > 0 for all x . Let A be the function such that A ( x ) equals the area between the graph of f and the x -axis on the interval [0 , x ]. a) Draw a picture of this for some value of x . Label A ( x ). For a small value of h , also indicate A ( x + h ) in your picture. What is A (0)?

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