Re: what is the reason that made newton to invent calculus?

From: yogesh (ypjofficial_at_indiatimes.com)
Date: 09/21/04 

Date: 21 Sep 2004 01:52:00 -0700

> Probably because it's so hard to divide by zero and have the results
> make any sense. Recall that one way of defining the derivative is the
> slope of the tangent line. The slope of anything is:
>
> Rise y2 - y1 f(x + dx) - f(x)
> ----- = -------- = ----------------, where dx is delta x.
> Run x2 - x1 dx
>
> The slope of the secant line is defined by the 3rd formula. If you
> take
> dx to zero, you get the tangent line. But the slope is infinite i.e. a
> vertical line. Houston, we have a problem!
>
> So Newton decided to get as close as he could without going infinite
> (postal?).
> If you got dx close enough to zero, slope secant line = slope tangent
> line in
> any case that matters.

Finding a rate of change can be undestandable.And anyone would be
satisfied by knowing the average rate of chage.
What impresses me about Newton is that he was not satisfied with the
average rate of change and went for further analysis.
Why Newton thought that the average rate of change and the
instantaneous rate of change would be different? Or what made Newton
to think so ?

(I think we are goind in a loop..back to the original question again..
and I know the definition of derivative , how it is calculated its
history etc..I just wanted to know the *genuis* thoughts which would
have touched Newton's mind while inventing the calculus..

)

regds,
Yogesh Joshi

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