Consider the function ne) 2 (4m i 4)7/3. a) Find the first, second, and third derivative of f. f'(m) I @- M) = mm) = an b) Compute f(1),f'(1),f\"(1) and fm(1). Give exact answers. f(1) = @- f'(1): @- M1) 2 mm = c) Find the Taylor polynomial of order three T3 of f at the base point a, = 1. T3(m) = @- d) Evaluate the size of the error made if T3 (0.4) is used to estimate f(0.4); namely, compute |f(0.4) T3 (0.4) |. Give your answer with an accuracy of six decimal places. Answer: Number