essay

Question

Let f (x) = x3.
(a) Estimate the values of f'(0), f'(½), f'(1), f'(2), and f'(3) by using a graphing device to zoom in on the graph of f.
(b) Use symmetry to deduce the values of f'(–½), f'(–1), f'(–2), and f'(–3).
(c) Use the values from parts (a) and (b) to graph f’.
(d) Guess a formula for f'(x).

(e) Use the definition of derivative to prove that your guess in part (d) is correct.