In a volume–maximization problem

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

In a volume–maximization problem, the volume

V

of a box has been expressed as a differentiable single-variable function

V(x)

after applying all constraints. Identify the mathematical condition that any interior value

x

must satisfy to be considered a candidate for the maximum volume.