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EXAMPLE 2 (a) If f(x) = 5x5 - 4x, find a formula for f'(x). 40 (b) Illustrate by comparing the graphs of f and f'. SOLUTION (a) When computing a derivative, we must remember that the variable is h and that x is temporarily regarded as 20 a constant during the calculation of the limit. lim f ( x + h) - f(x) -2 f' ( x ) = h-+0 h -20 lim [5( )3 - 4(x + h)] - [5x3 - 4x] = 1 h-+0 h Video Example () Tutorial lim 5 x + -4x - 4h - 5x + 4x Online Textbook =h-0 h lim =h-0 h lim ( =h-+0 + 15xh + 5h- - 4) (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)