- A visual demo of Newton's Method for pre-calculus students.
- Calculus, Geometry
- Middle School, High School, Community College / Lower Division
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An outstanding visualization! You can enhance your visualization by adding the following algebraic explanation to your comment section:
Suppose the point you choose is [c, f(c)].
In order to find the second guess, we need the equation of the tangent line at x=c, after which, we can find where it intersects the x-axis to obtain the second guess.
So, let t(x)=f'(c) x + k where t(x) is the equation of the tangent line.
We determine k as follows:
f(c) = f'(c) c + k
=> k=f(c) - f'(c) c
=> t(x)=f'(c) x + f(c) - f'(c) c
=> t(x)=f'(c) [x - c] + f(c)
We know the tangent line intersects the x-axis when t(x)=0.
0= f'(c) [x - c] + f(c)
=> x - c = - f(c) / f'(c)
=> x = c - f(c) / f'(c)
This last equation provides the next guess, that is, x as expected.