Trying to differentiate a function using fermat's way.

In summary, the conversation discusses differentiating a function and finding the equation of a line using two methods: the standard way used today and Fermat's method from the 1600's. The final equation obtained through both methods should be the same, but the speaker is unsure of their calculations. They eventually find the correct answer and the conversation ends.
  • #1
lost_in_phys
8
0

Homework Statement


I'm supposed to differentiate a function: (x^3) + 2x
Using the standard way used today, and then find the equation of the line so that it passes through (1,3).
So I did: 3(x^2) + 2
and then the final equation is y = 5x - 2 right?

Then I'm also supposed to differentiate and find the equation using fermat's method, and given from the readings we have, it's:

TQ = [E * f(x)]/[f(x + E) - f(x)]

***This is the equation described in "Early Seventeenth Century Work on The Calculus, p..345"***

and I should get the same thing, but I get [(x^2)+2]/[3x]

which for x = 1 would give y = 1

I got this by expanding everything and then eliminating opposites (ie +2x and -2x) and then ones with E I put to 0, because according to what I read, that's what we do.

What am I doing wrong?
 
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  • #2
lost_in_phys said:

Homework Statement


I'm supposed to differentiate a function: (x^3) + 2x
Using the standard way used today,
...um... this is less than clear... "used today"? Like, your teacher used it today in your class? Or what?

and then find the equation of the line so that it passes through (1,3).
So I did: 3(x^2) + 2
and then the final equation is y = 5x - 2 right?

Then I'm also supposed to differentiate and find the equation using fermat's method, and given from the readings we have, it's:

TQ = [E * f(x)]/[f(x + E) - f(x)]

***This is the equation described in "Early Seventeenth Century Work on The Calculus, p..345"***

Once again, this is rather less than clear. Are we supposed to know what book you are talking about? No, that's absurd... although a google search indicates that you might be using the book "Mathematical Thought from Ancient to Modern Times"... is that right?

and I should get the same thing, but I get [(x^2)+2]/[3x]

which for x = 1 would give y = 1

I got this by expanding everything and then eliminating opposites (ie +2x and -2x) and then ones with E I put to 0, because according to what I read, that's what we do.

What am I doing wrong?

I'm not really sure what your question is. You should try to reformulate your question in a way that is more understandable. This will help us to help you.
 
  • #3
sorry i was unclear, basically i was trying to differenetiate the function to find the slope using the old method described by fermat in the 1600's. Anyway, I ended up getting it, thx.
 
  • #4
I'm glad you got it. Cheers.
 

1. What is Fermat's way of differentiating a function?

Fermat's way of differentiating a function involves finding the derivative of a function by using the limit definition of a derivative. This method was developed by French mathematician Pierre de Fermat in the 17th century.

2. How is Fermat's way different from other methods of differentiation?

Fermat's way differs from other methods of differentiation, such as the power rule or chain rule, as it relies on the limit definition of a derivative rather than algebraic rules. It can be used to find the derivative of any function, including those that cannot be differentiated using other methods.

3. What are the steps involved in Fermat's way of differentiation?

The steps involved in Fermat's way of differentiation are as follows:1. Determine the difference quotient of the function.2. Take the limit of the difference quotient as the change in x approaches 0.3. Simplify the resulting expression to find the derivative.

4. When should I use Fermat's way of differentiation?

Fermat's way of differentiation should be used when other methods, such as the power rule or chain rule, are not applicable. It is also useful for finding derivatives of functions with multiple variables or complex functions.

5. What are the limitations of using Fermat's way of differentiation?

While Fermat's way of differentiation is a powerful method that can be used for any function, it can be time-consuming and tedious. It also requires a thorough understanding of limits and may not always yield the most efficient or accurate result. Additionally, it can be difficult to apply to functions with multiple variables or those that are not continuous.

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