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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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# Homework Help: Trying to differentiate a function using fermat's way.

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