Presentation is loading. Please wait.

Presentation is loading. Please wait.

Method for finding tangent lines Pierre de Fermat (1601-1665)

Similar presentations


Presentation on theme: "Method for finding tangent lines Pierre de Fermat (1601-1665)"— Presentation transcript:

1 Method for finding tangent lines Pierre de Fermat ( )

2 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

3 Fermat’s Similar Triangles Tangent line at point T T

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

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

6 Fermat’s Similar Triangles O A T

7 O A T P B

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

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

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

11 O A T P B s

12 O A T P B s

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

14 Example

15

16

17 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

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


Download ppt "Method for finding tangent lines Pierre de Fermat (1601-1665)"

Similar presentations


Ads by Google