Question as in title. I know a linear combination of continuous functions is continuous, but am not sure about twice continuously differentiable functions.
2026-03-30 17:37:06.1774892226
Is a linear combination of twice continuously differentiable functions twice continuously differentiable?
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Yes. Linear combinations with constant coefficients do not harm continuity or differentiability in any way. With other functions as coefficients, they have to display the same properties that the functions you have (because you can look the combination in both ways).