Function Generation

Colleges & Universities Massachusetts Institute of Technology
1

<p>I was just wondering how one could go about generating functions based on parameters, such as,</p>

<p>f(x) shoudl have minimum at (a,b)
and max at …
and intercept x axis at …
and …</p>

<p>My main ideas are basically you have 2 differential equations?</p>

<p>like if they want concave up or down at certain poitns {r, s, t}, you would have something like:</p>

<p>d^2y/dx^2 = (x-r)(x-s)(x-t)</p>

<p>and then you would have to solve down to dy/dx, and then finally y = …</p>

<p>any tips?</p>

<p>This is for an idea i had where some one gives you graph of function, and you can generate the function itself.</p>

2

<p>I think you might be more interested in functional equations, there are lots of Olympiad level problems on the subject that will take a good amount of time to solve and give you a feeling of satisfaction when you actually prove the anser.</p>

3

<p>based on the number of points of maxima and minima, you can deduce the degree of the polynomial function. Once youve done that, write the function out in the general form and use the rest of the conditions to produce linear equations involving the coefficients. You will definitely have enough equations if all the points of max, min and the intercepts with axes are given</p>

4

<p>amrik:</p>

<p>I wish. I can’t even get past AMC 12. Lets just say that math competitions aren’t my strong point, though I wish they were. So instead, I just try to study higher level math, which is more interesting to me, especially Calculus, which is my favority subject so far in life.</p>

5

<p>sagar, go to <a href=“http://www.artofproblemsolving.com/[/url]”>http://www.artofproblemsolving.com/&lt;/a&gt;&lt;/p&gt;

<p>these kind of questions belong there!</p>