Math Is Fun Forum

joetrivolio

Guest

calculating slope of any curve

how can you calculate the slope of any curve that is not defined by a function f(x)?

my method is, for example, if i have 100 points on an S-curve, then i take 100 different slopes (from point to point, for example between x1y1 and x2y2, then x2y2 and x3y3, then divide sum of total gradients by number of slopes taken to get an average slope). is this the best method to calculate a slope of any curve.

thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: calculating slope of any curve

Hi joetrivolio;

Welcome to the forum.

When you talk about an average slope of a curve between 2 points it means using the formula

That is the average slope of f(x) between 2 points. I am not familiar with you idea at all where did you get it?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

joetrivolio

Guest

Re: calculating slope of any curve

hi, i didn't get my idea anyway, i came up with it. for example, if you were asked to draw a cumulative frequency polygon, and were asked to calculate the rate of change of the s-curve you ended up drawing, could you not simple calculate the slopes between every point and then take the average slope of all of them?

i know about slope between two points to get slope of f(x), but it isn't accurate. also, what if i wanted to find the area under such a curve? is there a better method than manually doing it, i.e. making trapeziums underneath it

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: calculating slope of any curve

Hi joetrivolio;

I am not sure. I can't find anything like that. If you made it up then it is not likely there is going to be.

i know about slope between two points to get slope of f(x), but it isn't accurate.

Because it is an average it is always going to be somewhat inaccurate. There is only so much info about a sequence that can be stuffed into a single number.

what if i wanted to find the area under such a curve? is there a better method than manually doing it, i.e. making trapeziums underneath it

The answer is loosely, Yes! First I have to ask you some questions. How many points do you have? Do you have access to any math software such as Mathematica , Maple , Derive, Maxima etc? What technology do you use?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.