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A derivation for the intersection of the tangent to a curve at a and the x-axis?
Please outline a nice derivation of the fact that, if a function f is differentiable at x=a and continuous, then the point of the intersection of the tangent to f at a intersects the x-axis at the point
x= a - [f(a)/f'(a)].
1 Answer
- ?Lv 710 years agoFavorite Answer
This is the Newton-Ramphson Method , it is a numerical Method.-
suppose you have y =f(x) , the tangent line has a slope m= dy/dx at x=a , so m = f´(a) .- The line passes by point P (a, f(a) ) , so its equation is y-f(a) = f´(a) (x-a)
x intercept is when y=0 , so x = a- ( f(a) /f´(a) )