I've encountered this problem:
Let $f(x)=|x-p|+|x-15|+|x-p-15|$, where $0 < p < 15$. Determine the minimum value taken by $f(x)$ for $x$ in the interval $p \leq x\leq15$.
I'm not sure what the question is asking for, because at least the way I understand it, there is no minimum value of x! You can sub any real number x into the function, and it will work. At most, given the that $p \leq x\leq15$, the minimum value of x is that 1>x>0!
Can someone tell me what the question wants me to do, without telling me how to solve the question?