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Published byAlma Nevils Modified about 1 year ago

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Method for finding tangent lines Pierre de Fermat ( )

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Life and work Interesting facts: – He was a French lawyer – He pursued maths as a hobby – He is known as the “Prince of Amateurs” – His contribution to calculus was less well known. Contribution to calculus development: – determining maxima, minima – finding tangents to various curves – Evaluating area under a graph

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Fermat’s Similar Triangles Tangent line at point T T

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Fermat’s Similar Triangles T(x,y) A(x,0) s y O(x-s,0)

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Fermat’s Similar Triangles To calculate value of s, he used a technique based on similar triangles.

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Fermat’s Similar Triangles O A T

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O A T P B

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Set the length OA =s, OB = s + E O A T P B s E

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Fermat’s Similar Triangles O A T P B s E

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O A T P B s E O A T P B s

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O A T P B s

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O A T P B s

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Example Let’s find the tangent of the curve at (2,4)

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Example

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Let y = 4x+c be the equation of the tangent at point (2,4) By substituting (2,4) in the equation, 4=4 (2) + C C = -4

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Example Therefore, the equation of the tangent is Y = 4 x -4

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