Let f(x) ≡ (1 – x)^b + b a^b-1 xø (x) ≡ x^c – c Β^c-1 xwhere b ≧ 1, c ≧ 1, 0 ≦ α ≦ 1, 0 ≦ β ≦ 1, and x is assumed to lie in the range (0, 1). By differentiation, or otherwise, it is easily shewn that f(x) and ø (x) have minima when x = 1 – α and when x = β, respectively. Hence(1 – x)^b + a^b-1 x ≧ b a^b-1 + (1 – b) a^bx^c β^c-1 x ≧ (1 – c)β^c.