# Calculus in Games

**Calculus**Level 3

Max is a virtual character in a particular 2D game. He has the choice of \(2\) functions (curve) to walk on to collect coins.

**Road 1**\(\frac{x^3}{6} + \frac{1}{4x}\) from \(0 \leq x \leq 5\) where there are \(20\) coins evenly distributed along this arc.**Road 2**\(\ln {(\sec {x}})\) from \(0 \leq x \leq \frac{\pi}{3}\) where there is \(1\) coin along this arc.

Which function is the most coin-to-distance efficient for him to take? (Meaning which function should he walk to gain more coin in a unit distance?)