Trying to differentiate a function using fermat's way.

[lost_in_phys]

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?

 

[olgranpappy]

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.

 

[lost_in_phys]

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.

 

[olgranpappy]

I'm glad you got it. Cheers.