jmc

Question

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 x15.

Accepted Answer

Since 0 < p x 15, the absolute values simplify to f(x) = (x-p) - (x-15) - (x-p-15) = -x+30.The value of this expression is minimized when x=15, giving -15+30=15.