tangent line problem - descartes vs fermat
TRANSCRIPT
Tangent Line Problem - Descartes vs Fermat
Tangent Line\
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Is it possible to find the tangent line at any point x=a?
Method Method
Example 1 - Find the slope and then write an equation of the tangent line to the function y = x2 at the
point (1,1) using Descartes' Method. '2-• i - n- M _xc u " 1L -~T- ~ O
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Example 2 - Find the slope slope and then write an equation of the tangent line to the function y = x2
at the point (1,1) using Fermat's Method. . ^- [ -
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*- ) " /Example 3 - Find an equation for the tangent line of y = V3x passing through the point (3,3) using
Descartes' Method.
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Example 4 - Find an equation for the tangent line of y — V3x passing throu^rTthe"poInt(3,3) using
Fermat's Method.
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slope (t)
Q Q'Example 5 - Write an equation of the tangent line to the ctFrve y = V4x at the point A = (1,2) using
either method.
Descartes heavily relied on standard algebraic manipulation which made his method limited to simple
algebraic curves.
Fermat's approach could be used on a wide variety of curves because of the use of a limiting process.
Sources:
http://math.kennesaw.edu/~jdoto/13.pdf
http://users.etown.edU/s/sanchisgr/HistoryOfMathematics/Calculusl/Worksheets/W3.pdf
Bauldry, W. (2009). Introduction to real analysis: an educational approach, (pp. 42-44). Hoboken, NJ: John Wiley & Sons, Inc.