Fermat's method of calculus
I've attached my question as a file and here is the resource I was looking at https://cedar.wwu.edu/cgi/viewcontent.cgi?article=1012&context=wwu_honors

what is the question?

you are asking why does this actually work even after answering the same. But you are also sayng you wont get anywhere

Your question is very vague. Please clarify.

my question basically is why does this method work to give you a tangent line? specifically the steps where you divide by e and then plug 0 in for e
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can you explain further the last part you wrote?

In essence, this procedure allows to find the xaxis cross value as a limit operation. When we replace T(x+epsilon) by f(x+epsilon) we are thinking of a sufficiently small epsilon for this to make sense. This is a limit operation t that is quite literally based on Taylor first order approximation.

I added another explanation.
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