# Finding the ratio of the fluxion of x using Newton's method

• BurtZ
Given x = f(t), the fluxion of x is df/dt. In summary, we discussed the concept of fluxions in the context of Newton's synthetic method. A fluxion is the speed at which speed increases, or the derivative, and can be calculated using the function x = f(t) as df/dt. The conversation also mentioned the importance of following PF guidelines and posting one's own attempt before seeking assistance.
BurtZ
Homework Statement
Find the ratio of the fluxion of x to the fluxion of 1/x using Newton's synthetic method of fluxions.
Relevant Equations
None.
I was asked to find the ratio of the fluxion of x to the fluxion of 1/x using Newton's synthetic method of fluxions. I do not understand how to do this.

I believe you. But PF guidelines require you post your own attempt before assistance is allowwed.
So: what are we talking about ? What is a fluxion a la Newton (sounds like a recipe ) and how does one calculate it ?

##\ ##

BvU said:
I believe you. But PF guidelines require you post your own attempt before assistance is allowwed.
So: what are we talking about ? What is a fluxion a la Newton (sounds like a recipe ) and how does one calculate it ?

##\ ##
A fluxion of the quantity x (which is dependent on time) is the speed at which speed increases.

Essentially it seems to be the derivative.

## 1. What is Newton's method?

Newton's method is a mathematical algorithm used to find the roots of a given function. It is based on the concept of using the derivative of a function to approximate the roots.

## 2. How does Newton's method work?

Newton's method works by starting with an initial guess for the root and then using the derivative of the function at that point to calculate a new and hopefully better approximation. This process is repeated until the desired level of accuracy is achieved.

## 3. What is the purpose of finding the ratio of the fluxion of x using Newton's method?

The ratio of the fluxion of x is used to determine the rate of change of a function at a specific point. This information can be useful in many scientific and mathematical applications, such as optimization problems and numerical analysis.

## 4. How is the ratio of the fluxion of x calculated using Newton's method?

The ratio of the fluxion of x is calculated by taking the derivative of the function and then using Newton's method to find the root of the derivative. This root represents the ratio of the fluxion of x at the given point.

## 5. What are the limitations of using Newton's method to find the ratio of the fluxion of x?

Newton's method can only find an approximation of the root, not the exact value. It also requires an initial guess for the root, which may not always be accurate. Additionally, it may not converge or may converge to a wrong root if the function is not well-behaved or has multiple roots.

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