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A Funcion about 3D Geometry

Source: 1984 National High School Mathematics League, Exam One, Problem 8

February 22, 2020
functiongeometry3D geometrytetrahedron

Problem Statement

Lengths of five edges of a tetrahedron are 11, while the last one is xx. Its volume is F(x)F(x). On its domain of definition, we have (A)\text{(A)} F(x)F(x) is an increasing function, it has no maximum value. (B)\text{(B)} F(x)F(x) is an increasing function, it has maximum value. (C)\text{(C)} F(x)F(x) is not an increasing function, it has no maximum value. (D)\text{(D)} F(x)F(x) is an increasing function, it has maximum value.
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