Math Is Fun Forum

Tredici

Member

Registered: 2005-12-12

Posts: 28

A Simple Problem (But I don't know how to explain it)

Hi All,

This is probably going to be a very simple problem for you masterminds. Please excuse my ignorance here guys but I'm completely out of practice and haven't done this sort of stuff for about five years.

I need a simple function which will produce a value of 0 when 0 is passed into it, a value of 20 when 50 is passed into it, and a value of 0 when 100 is passed into it.

Sounds so simple, but I've literally spent hours getting something even vaguely close. I've gotten closest with one function, a depiction of which is attached to this post.

Thanks in advance for any help at all.

Cheers, David

Last edited by Tredici (2008-04-15 02:18:44)

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: A Simple Problem (But I don't know how to explain it)

f(0)=0
f(50)=20
f(100) = 0

Could you maybe use a trig function? Like:

Or do you just want a quadratic like

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Tredici

Member

Registered: 2005-12-12

Posts: 28

Re: A Simple Problem (But I don't know how to explain it)

Thanks a bundle bossk172. I was indeed looking for a quadratic. Do you mind me asking how you came up with it?

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: A Simple Problem (But I don't know how to explain it)

You connect those points, then you could compare the graph to other types of funcions'

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: A Simple Problem (But I don't know how to explain it)

You can play with bossk's functions here: Function Grapher and Calculator

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: A Simple Problem (But I don't know how to explain it)

Lagrange Polynomials

For your problem, the L_j are:

So that the final polynomial is:

This simplifies to bossk171's polynomial.

Newton also has a polynomial interpolation method if you want to look that up.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."