EXAMPLE 2 (a) If f(x) = 3x3 - 4x, find a formula for f'(x). (b) Illustrate by comparing the graphs of fand f. SOLUTION (a) When using this equation to compute a derivative, we must remember that the N variable is h and that x is temporarily regarded as a constant during the calculation of the limit. f'( x ) = lim f( x+ h ) - f ( x ) h - 0 m = lim - 4(x + 1 ) - [3 x 3 - 4x ] h - 0 3x3 + = lim - 4x - 4h - 3x3 + 4x h - 0 in = lim h - 0 C Video Example () = lim h - 0 (b) We use a graphing device to graph f and f' in the figure. Notice that f'(x) = 0 when f has horizontal tangents, and f'(x) is positive when the tangents have positive slope. So these graphs serve as a check on our work in part (a)