differential equation: given f(x), show that f(x), f'(x), and f"(x) are continous for all x

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Dutsky Kamdon
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differential equation: given f(x), show that f(x), f'(x), and f"(x) are continous for all x

Let
f1(x) = 1 + x^3 for x ≤ 0 ,1 for x ≥ 0
f2(x)= 1 for x ≤ 0, 1 + x^3 for x ≥ 0
f3(x)= 3 + x^3 for all x.

show that
a) f, f' , f", are continous for all x for each f1, f2, f3.

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