(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The following five points lie on a function:

(1,20) (2,4) (5,3) (6,2) (10,1)

Find an equation that passes through these points and has these features:

a. There are three inflection points

b. There is at least one local maximum

c. there is at least one local minimum

d. at least one critical point is not at a given point

e. THE CURVE IS CONTINUOUS AND DIFFERENTIABLE THROUGHOUT

f. the equation is not a single polynomial, but must be a piecewise defined function

The easiest thing we've tried is to put the cubic parts of the function outside of points from 1 to 10 but we can't seem to make it differentiable. We've tried everything that we could think of... PLEASE help, as this is due tomorrow and we've exhausted all of our options!!!

2. Relevant equations

3. The attempt at a solution

I know that the slope at the connecting points of each part of the piecewise function must be equal, but I can't figure out how to make that happen/work. I've tried a variety of linear equations, but those are not differentiable. I'm really stuck, and have been working on this problem for, literally, DAYS. Please help in any way you can!!!- with either the equation, or tips/advice/help for how to make the derivatives equal without messing around with the whole function. THANKS!

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# Homework Help: Please help!- MYSTERY CURVE

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