Show that the Linear Approximation to f (x) = x at x = 9 yields the estimate

Question:

Show that the Linear Approximation to f (x) = √x at x = 9 yields the estimate √9 + h − 3 ≈ 1/6 h. Set K = 0.01 and show that |f′′(x)| ≤ K for x ≥ 9. Then verify numerically that the error E satisfies Eq. (5) for h = 10−n, for 1 ≤ n ≤ 4.