essay

Question

Let f (x) = x2.
(a) Estimate the values of f'(0), f'(½), f'(1), and f'(2) 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), 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.