To the reader: There are members on this forum who insist on spamming my threads with ignorant and/irrelevant comments. Please read my ignore list before continuing..

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Since some on this forum seem unfamiliar with the concept of function (especially as regards the derivative) I thought I'd provide a direct reference link for those new to the subject.

**FUNCTION**
(It is with a view to helping John Gabriel understand the role of curvature, who at present seems to be only vaguely familiar with the concept of a straight line, but can (almost) calculate the

**slope** correctly ...

However, the reader may need to refer first to the

**equation of a straight line**....

Attachment 1138
The correct slope is given by

where m = 0.

(John Gabriel's red line is too long and in the wrong vertical position because of m)

One then takes the limit on n->0 for the linear derivative:

,

which eliminates (i.e. makes insignificant) higher orders of f(x) (i.e., curvature) when n gets small enough for an arbitrary function f(x) at an arbitrary position x ; i.e., (x, f(x)) = (x, y(x)) ..

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