Student Portal | Miami Dade Ct X Content Section_2.8_Derivatives_as_F X + C webassign.net/web/Student/Assignment-Responses/last?dep=29463627 0 * M Paused 3 DETAILS SCALCET9 2.8.AE.002. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER EXAMPLE 2 Video Example ) (a) If f(x) = 2x5 - 4x, find a formula for f'(x). (b) Illustrate this formula by comparing the graphs of f and f'. SOLUTION (a) When using f(x) = lim _ )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 = lim - 4(X + 1 ) - 12x 3 - 4 x ] h 2x3+ lim - 4x - 4h - 2x3 + 4x h lim n lim (b) We use a calculator 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). MacBook AirStudent Portal | Miami Dade Cc X Content X "* Section_2.8_Derivatives_as_F X C 0 webassign.net/web/Student/Assignment-Responses/last?dep=29463627 11 Dey i diaw paAN 9. DETAILS SCALCET9 2.8.057.MI. Let f(t) = t. For a + 0, find f'(a). f'(a) Need Help? Read It Watch It 10. DETAILS SCALCET9 2.8.039