MathDB
Least possible value

Source: UMD 2023 I #21

October 22, 2023
algebraUMD

Problem Statement

Let a,b,c,d,ea, b, c, d, e be real numbers such that a<b<c<d<e.a<b<c<d<e. The least possible value of the function f:R→Rf: \mathbb R \to \mathbb R with f(x)=∣x−a∣+∣x−b∣+∣x−c∣+∣x−d∣+∣x−e∣f(x) = |x-a| + |x - b|+ |x - c| + |x - d|+ |x - e| is a. e+d+c+b+ab. e+d+c−b−ac. e+d+∣c∣−b−ad. e+d+b−ae. e+d−b−a \mathrm a. ~ e+d+c+b+a\qquad \mathrm b.~e+d+c-b-a\qquad \mathrm c. ~e+d+|c|-b-a \qquad \mathrm d. ~e+d+b-a \qquad \mathrm e. ~e+d-b-a
Back to ProblemsView on AoPS