You own a ski resort. In the winter, the amount of customers go up. In the summer, the amount of customers go down.
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Rational function can be used in real life in modeling multi-person work problems.
Your age is a linear function (of time).
Differentials can be used to approximate a nonlinear function as a linear function. They can be used as a "factory" to quickly find partial derivatives. They can be used to test if a function is smooth.
As with most advanced math, if your "real life" involves engineering work, you will use such math; otherwise, you will hardly have anything to do, in this case, with polynomial functions.
electricians use the Square Root function when connecting 3 way outlets with the electral current of an intel processor.