## What is functional?

A `functional`

takes a function and returns an output value. For example, a functional can calculate the length of a curve. The curve path is defined by a function. Another common example in machine learning community is that an Entropy functional will take any probability density function and return a scalar value representing the entropy of `x`

under the density.

Like in conventional calculus, we seek a function `y(x)`

that maximizes the value of the functional `F(y)`

. For example, the shortest path between two points is a straight line(i.e., the function describing the curve path will be a straight line equation).

How much would `F(y)`

change if we make a small change `(x)`

to the function `y(x)`

?