Let f(x) = x3. (a) Estimate the values of f (0), f(), f(1), and f(2) and f

Question:

Let f(x) = x3.
(a) Estimate the values of f’ (0), f’(½), f’(1), and 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’ (-1/2), f’ (-1), and f’ (-2) and f’ (-3).
(c) Use the values from parts (a) and (b) to graph f1.
(d) Guess a formula for f’(x)
(e) Use the definition of a derivative to prove that your guess in part (d) is correct.