Manuscript 1

Manuscript 1 - Danielle M Henak Calculus II David Sharpe...

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Danielle M. Henak Calculus II September 26, 2007 David Sharpe Manuscript 1 Considering that on the parabola y=x 2 , there are two points A and B which can be connected by a line. If the x value for A is c and the x value for B is d, the slope of the line connecting these two points would be equal to = ΔyΔx d - - = - + - = + 2 c2d c d cd cd c d c . Because this line must run through the middle of the parabola, there must be some point on the parabola that has a tangent line equal to this slope. Therefore, = = + dydx 2x d c = + x d c2 for the x value of a point C. Thus, there are the points A(c,c 2 ), B (d,d 2 ) and C ( + d c2 , 14d + + 2 cd 14c2 ). The area bounded by the line AB and the curve of the function y=x 2 , can be found by taking the area of the trapezoid created by the lines x=c, x=d, AB, and the x-axis subtracted by the area under the y=x 2 curve. In a mathematical equation that would look like this, considering that the equation for the area of a trapezoid equals ( 12h b + ) 1 b2

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Manuscript 1 - Danielle M Henak Calculus II David Sharpe...

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