We can also prove that 𝑓𝑓(𝑥𝑥) ≤ 𝑥𝑥 for all 0 ≤ 𝑥𝑥 ≤ 2 and 0 < 𝑚𝑚 ≤ 1. The first derivative of 𝑓𝑓(𝑥𝑥) at 𝑥𝑥 = 0 is always less than or equal to 1, with equality if and only if 𝑚𝑚 = 1, as shown by the inequality of arithmetic and geometric means.