Isn't it infinity?

Calculus Level 3

How many functions are there such that \(f''(x)>0\) for every \(x>0\), \(f(1)=-5\) and \(f(2)=-11\) and f(0)=0 ? If the number of functions is \(n\), then submit your answer as \(n!+n-1\).

Notation: \(f''(x)\) means second derivative of \(f(x)\).

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