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hw11-8-1 - Homework 11/8 This worksheet is about locating...

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Homework 11/8 This worksheet is about locating the root of the function f ( x ) = 0 . 5 x 3 - x - 0 . 5 e - x , which is graphed below. You will end up with a lot of messy decimals as you work these problems. Keep every decimal accurate to at least 5 places. –2 –1 1 2 –2 –1 1 2 1. Assume that x = 1 is the root. (This is wrong, but that’s ok.) (a) Find f (1). (If you get zero, then 1 is the root and you can quit.) (b) Find the equation of the tangent line at x = 1. (c) Graph the tangent line on the graph of f provided above. (d) Find where the tangent line crosses the x -axis. 1
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2. If your last answer was not x = 2, then go back and find your mistakes. If it was x = 2, assume that x = 2 is the root. (This is wrong, but that’s ok.) (a) Find f (2). (If you get zero, then 2 is the root and you can quit.) (b) Find the equation of the tangent line at x = 2. (c) Graph the tangent line on the graph of f provided above. (d) Find where the tangent line crosses the x -axis.
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