a Show that f(x) 0 has a root in the interval 3 4, 3 5 b Find f '(x) c Taking 3 4 as a first approximation to , apply the NewtonRaphson procedure once to f(x) to obtain a second approximation for , giving your answer to 3 decimal places f(x) ln (3x 4) x 10, x 3

Question: a. Show that f(x) = 0 has a root in the interval [3.4, 3.5]. b. Find f'(x). c. Taking 3.4 as a first approximation

a. Show that f(x) = 0 has a root α in the interval [3.4, 3.5].

f(x) = ln (3x 4) x + 10, x > 3

b. Find f'(x).

c. Taking 3.4 as a first approximation to α, apply the Newton–Raphson procedure once to f(x) to obtain a second approximation for α, giving your answer to 3 decimal places.

f(x) = ln (3x 4) x + 10, x > 3

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