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

Dutsky Kamdon's picture

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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