1. The problem statement, all variables and given/known data Solution: Let f(x) = x^3 - 3x^2 + 4x + 1 f'(x) = 3x^2 - 6x + 4 = 3(x-1)^2 + 1 > 0 Therefore f(x) is always monotone increasing. From f(0) = 1, x> 0 and f(x) > 1 and therefore proves the inequality. 2. Relevant equations 3. The attempt at a solution I understand how they got the derivative and how they got it into vertex form, but I don't know how by putting it into vertex form it proves that f(x) is always monotone increasing? Can someone please help me understand this method?