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**glambeth** @HallsOfIvy Okay, that makes sense I just used what plato showed me to show the function is continuous at 0. This makes sense so both the first and second derivative are 0. To compute the second derivative you just do the same thing but set f(x) = x^2g(x), right?

So, if f(x) was defined as x^2 g(x) the second derivative at 0 would just be g(x) = 1, or would it be defined. I guess i'm not sure if lim h-> 0 of g(h) is 1 or undefined. I'm starting to think it is undefined as the rationals are dense in R; hence, its oscillating between -1 and 1. Right?