Which Polynomial Function Are You?

We all start out as rosy-cheeked babies, drooling from our mouths as our pudgy hands grapple at our mothers’ faces. We’ve begun our lives as pure as can be; we only know of love and our parents pinching our chubby cheeks.

We enter the children phase where the other gender has cooties, and everything we see is a question waiting to be answered. “Mama, how are babies born? Daddy, why is the sky blue?” We accept our parents’ answers as gospel, but it’s also at this point where we realize that parents can be wrong. The protective shell we’ve been born in starts to crack.

Then, teenage-hood strikes in all of its acne-covered glory. The pressures of sports, classes, significant others hit you. A teen’s daily rhetoric consists of, “Oh my God, I’m going to kill myself, I can’t take this test… Oh my God, fuck it, just screw it, screw everything.” Suddenly, we’re all cemented in the sand while waves of cold ocean water sprinkled with AP exams and SATs douse us.

Jobs, heartbreak, lessons learned, rejections, acceptances  — we’ve come to adulthood. Adults are now accustomed to the 9-to-5 grind in their cubicles and briefcases in hand, before hopping into their car to eat dinner with their family and go to sleep. Divorces are a common occurrence, and the bills just keep piling up on the dinner table.

Over our lives, we’ll have shifted from a toothless-grinning cherub to a grown-up with perpetual under-eye circles. Daily pressures — significant others, jobs, financial issues, heartbreak — will have molded us from the kid who questions everything to an adult whose only question is, “What’s my purpose?” But, I truly believe that if you strip away these complex layers of anyone above the age of ten, you will find a golden core of passion and love that we were born with.

Now, consider the function x^3 + 5x^2 + 7x + 2 . After deriving this function, you get 3x^2 + 10x + 7. And after deriving again, you get 6x + 10. Derive again — 6. And finally, 0. We stripped a complex hyperbolic function with several characteristics (three roots, two extrema, etc.) to 0, the simplest of functions.  Essentially, the backbone of this equation is y = 0. Isn’t that funny? That this equation with all of its curves and points can be derived back to a horizontal line? It might be absurd, but this idea applies to people, too. After removing all the baggage — the jobs, the bills — that we complex human beings are under, I truly think we all have a raw core of love and passion. Right now we are the cubic polynomial, but we can be stripped back to a constant.

Screen Shot 2017-04-16 at 10.29.24 AM
The function mentioned above and its derivatives.

Maybe as we grow up, our degree changes. As babies, our function is y = 0. But as we progress through life, as the pressures pile on us, we go from y = 0, to y = x^2, to y = x^6, with more extrema, more roots, and more facets. Yes, it seems foolish, but I like to think that there’s a parallel between humans and mathematics.

But, what about trigonometric equations?  Sine and cosine? If you derive a y = sinx, you get y = cosx. Derive again — -sinx. Again — -cosx. You’re thrown into a continuous cycle of ups and downs, no matter where you start.

Screen Shot 2017-04-16 at 10.36.39 AM
y = sinx and its derivatives.

Maybe, this could apply to the cycle of life — the albeit cliche but legitimate concept that life always has its ups and downs, since we were born as those little red-cheeked babies to who we are now: fully-functioning adults with a plethora of worries and burdens, with y = 0 within us all.

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3 thoughts on “Which Polynomial Function Are You?

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