TM-MO 2015 Problem 4

Find the max and minimum without using dervivate: $\sqrt{x} +4 \cdot \sqrt{\frac{1}{2} - x}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.