Question

Prove the inequality, log (1 + x) > x – x²/2 for all x in R⁺

Answer 1

⇒ f(x) is strictly increasing in (0, ∞)

Thus f(x) > f(0)

⇒ log(1 + x) – x + x²/2 > 0

⇒ log(1 + x) > x – x²/2