Expert: Rekha Gupta - 5/6/2004

Question
I have been provided with a graph by customers of our based on their research into the lives of their products.  I'd like to develop an equation for this curve so that I can use it for our own products, but can't remember the method for this.  Given multipe points on a curve (one bend) how do I get the equations to this curve?

Answer
I don't remember exactly which method can be used to develop an equation from a given curve, may be a calculus expert can help you.

Some key points that can help you find a solution:
1. If there is one bend (means maxima or minima), then the equation must have degree 2, two extremas degree 3, and so on.
2. Now write a general equation like:
f(x) = y = ax^2 + bx + c       2 degree, or
f(x) = y = ax^3+bx^2+cx+d=0       3 degree  etc
3. Read as many sets of x and y from the graph as there are number of constants (a,b,c,d etc)
4. Substitute the values of x and y to get several equations in terms of a,b,c and d.
5. Now solve those equations to get these constants.
6. At last substitute back these values of a,b,c,d in the general equation, you will get the equation of curve.