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Is it possible to find the slope of a curve at a point without using calculus?

okarin
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    If it is a circle or straight line, then yes... – Berci Jan 13 '14 at 01:16
  • If the point is a local minimum or maximum and the curve has a well-defined slop at that point, then it'll be zero.... – fgp Jan 13 '14 at 01:22
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    Yes, for an algebraic curve: 1) Translate the curve so that the point you want is the origin. E.g. If the point is $(a,b)$ change coordinates to $x=x-a$ and $y=y-a$. 2) Remove all the terms that are not of degree $1$. – OR. Jan 13 '14 at 01:25
  • Probably, you will need a calculus$\phantom{}_1$. Whether or not it is differential calculus (or it's related integral calculus). I assume that you mean differentiable calculus (as do most people in this context). That said, the form that differentiable calculus takes is probably inevitable in certain ways. You could develop the subject without limits, but I do not recommend this at the moment.. – Baby Dragon Jan 13 '14 at 01:33
  • @ABC: You need to post your comment as an answer with more detail. I'm mulling it over in my head and it seems like a great answer. –  Jan 13 '14 at 01:35
  • @okarin : in addition to Berci's answer, you can find the vertex of a parabola by completing the square (not calculus), and at the vertex the slope is zero. – Stefan Smith Jan 13 '14 at 03:00
  • @okarin: another answer is any even function ($f(-x) = f(x)$) for all $f$. If you know $f'(0)$ exists (which may not require knowing any calculus, e.g. if $f$ is a polynomial), then $f'(0)=0$. – Stefan Smith Jan 13 '14 at 03:02

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Slope of a curve at a specific point MUST be a limit, which I am not sure whether you classify as calculus or not. Slope is by definition a function of two distinct points, and the only interpretation of "slope of a curve at a point" is that of two points approaching each other along the curve.

If you are not allowed to use limits, then no because both points have the same x and y coordinates, causing a 0/0 evaluation which is meaningless.

laughing_man
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