Tangent Line Problem - Descartes vs Fermat Tangent Line \ •„ , 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 = x 2 at the point (1,1) using Descartes' Method. ' 2 - •i- n- M _xc u " 1L -~T- ~ O < ft. c- aJash'tuJHp^X (/VU-^C^IM » -TBK>G&f?iT hfts Example 2 - Find the slope slope and then write an equation of the tangent line to the function y =x 2 at the point (1,1) using Fermat's Method. . ^- [ - pa sr p't
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Tangent Line Problem - Descartes vs Fermat
Tangent Line\
•„ ,
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
<ft.
c-aJash'tuJHp^X (/VU-^C^IM » -TBK>G&f?iT hfts
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. . ^- [ -
pa sr
p't
*- ) " /Example 3 - Find an equation for the tangent line of y = V3x passing through the point (3,3) using
Descartes' Method.
X -
Example 4 - Find an equation for the tangent line of y — V3x passing throu^rTthe"poInt(3,3) using
Fermat's Method.
£
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.