The SDQ usually approximates the derivative much more closely than does the ordinary difference quotient. Let (x)

The SDQ usually approximates the derivative much more closely than does the ordinary difference quotient. Let ƒ(x) = √x and a = 3. Compute the SDQ with h = 0.01 and the ordinary difference quotients with h = ±0.01. Compare with the actual value, which is ƒ'(3) = 1/(2 √3).