Your age is a linear function (of time).
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Rational function can be used in real life in modeling multi-person work problems.
There are linear functions and there are quadratic functions but I am not aware of a linear quadratic function. It probably comes from the people who worked on the circular square.
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.
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.