Let = (1 + h) (1), where (x) = x 1 . Show directly that E = | '(1)h| is equal to h

Let Δƒ= ƒ(1 + h) − ƒ(1), where ƒ(x) = x⁻¹. Show directly that E = |Δƒ − ƒ'(1)h| is equal to h²/(1 + h). Then prove that E ≤ 2h² if −1/2 ≤ h ≤ 1/2. In this case, 1/2 ≤ 1 + h ≤ 3/2.