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Am i wrong to understand the equation as finding the maxima or the minima of an function?

However, the terms like functional and small real parameter confuses me.

I read up on whats a functional and cant really understand, so far my understanding of its, is that its a function where by instead of x, a varible, it consist of vectors like velocity and etc. Thus, am i wrong to say equation of KE is actually a functional?

On the part of small real parameter ε.. i just have no idea. All i can infer is that is a change in the vector. But where is there this need to implictly express such a term?

Is euler-lagrangian eq considered as tough for an undergrad?

i am seriously struggling with it...