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is there a way to do this problem or do i have to just guess and check. because by guessing and checking, i can't find the right answer

Name a function with the following characteristics: note: f prime means the first deriviative

f is continuous over the reals, f(0)=0, F prime (x) <0 if x<1, f prime(1) does not exist, f prime(x) <0 if x>1, the second deriviative of f(x) < 0 if x<1, the second deriviative of x >0 if x>1.

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