Let f(x) = x2.
(a) Estimate the values of f'(0),f'(1/2), f'(1) and f'(2) by using a graphing device to zoom in on the graph of .
(b) Use symmetry to deduce the values of f'(-1/2), f'(-1), and f'(-2).
(c) Use the results from parts (a) and (b) to guess a formula for f'(x).
(d) Use the definition of derivative to prove that your guess in part (c) is correct.