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Project 2 Mat 220

# Project 2 Mat 220 - Steve Klaus Mat 220 Project#2 1 A Graph...

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Steve Klaus 3/21/11 Mat 220 Project #2 1. A. : - + + + Graph Function x4 x 1x4 x 1 Determine any Horizontal asymptotes using the limit method From Chapter 2. B. - + - + = - + + + = - + + + x4 x 1x4 x 1 x4 x 1x4 x 1 1x21x2 1 xx4 1x4 1 xx4 1x4 = = 1 1 1 Determine all x values where the graph has horizontal tangents. Once done, find the tangent lines and re-graph the function with those tangent lines to confirm your results. This is problem 88 on pg. 206 Calculator Needed? Hogwash! C. = - + - + = - + + + fx x4 x 1x4 x 1 x4 x 1x4 x 112

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= [ - + - + + ] lny 12 lnx4 x 1 lnx4 x 1 = - + - - + + + dydx1y 121x4 x 14x3 11 1x4 x 14x3 11 = - - + - + + + ; dydx 124x3 1x4 x 1 4x3 1x4 x 1y = & = - + - + , = - - + - Since fx y y x4 x 1x4 x 1 So dydx 124x3 1x4 x 1 + + + - + - + 4x3 1x4 x 1x4 x 1x4 x 1 Now Set Equation Equal to Zero = - - + - + + + - + - + = dydx 124x3 1x4 x 1 4x3 1x4 x 1x4 x 1x4 x 1 0 = - - + - + + + - + - + = dydx 21124x3 1x4 x 1 4x3 1x4 x 1x4 x 1x4 x 1 0 21 = - - + - + + + - + - + = dydx 4x3 1x4 x 1 4x3 1x4 x 1x4 x 1x4 x 1 0 Now Do Bottom-Cross To Simplify =( - )( + + )( + )( - + ) - + ( - + ) dydx 4x3 1 x4 x 1 4x3 1 x4 x 1 x4 x 1 x4 x 1 ( + + ) + + = x4 x 1 x4 x 1 0 Then Multiply By The Reciprocal of the Denominator to The Other Side = - + + + - + - + - + + + + + - dydx 4x3 1x4 x 14x3 1x4 x 1x4 x 1x4 x 1x4 x 1x4 x 1x4 + + + + + = x 1x4 x 1x4 x 11 0 - + + + + + Multiply Right Side byx4 x 1x4 x 1x4 x 110 Because if you do one thing to one side you must do it to the there then you end up with
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Project 2 Mat 220 - Steve Klaus Mat 220 Project#2 1 A Graph...

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