27. [-/3.44 Points] DETAILS SCALCET8 2.8.AE.002. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER EXAMPLE 2 (a ) If f( x) = 2x3 - 2x, find a formula for f'(x). (b) Illustrate by comparing the graphs of f and f'. N SOLUTION (a) When using this equation to compute a derivative, we must remember that the 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 "- 2( x + 1 ) ] - [2x 3 - 2x ] = lim h - 0 10 + - 2x - 2h - 2x3 + 2x = lim h - 0 = lim Video Example() h - 0 = 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)