(Solved): For positive constants \( A \) and \( B \), the force between two atoms is a ...

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For positive constants \( A \) and \( B \), the force between two atoms is a function of the distance, r, between them: \[ f(r)=-\frac{A}{r^{2}}+\frac{B}{r^{3}}, \quad r>0 \] (a) For which values of \( r \) is \( f(r) \) positive? For which values is \( f(r) \) negative? Your answer should involve \( A \) and \( B \). Hint: There is no calculus in this part of the problem. It's just algebra. (b) Find all the values of \( r \) where \( f(r) \) has a global max or min on the interval \( (0, \infty) \). Your answer should involve \( A \) and \( B \). Be sure to verify that the function actually has a global max or min where you claim it does.