question can be seen in image provided

1)

If an arrow is shot upward on the moon with a velocity of 55 m/s, its height (in meters) after 1' seconds is given by H = 551' 0.83t2. (a) Find the velocity of the arrow after two seconds. :1 m/s (b) Find the velocity of the arrow when t = a. (c) When will the arrow hit the surface? (Round your answer to one decimal place.) (d) With what velocity will the arrow hit the surface? :1 m/s EXAMPLE 2 (a) If f(x) = 2x5 - 3x, find a formula for f'(x). (b) Illustrate by comparing the graphs of f and f'. 2 f SOLUTION X -2 2 (a) When using this equation to compute a derivative, we must remember that the variable is h and that x is -2 temporarily regarded as a constant during the calculation of the limit. -4 f'(x) = lim f ( x + h ) - f ( x ) h - 0 h -61 = lim 2 - 3(x + h) - [2x3 - 3x ] h - 0 20 h 2x3 + 15 - 3x - 3h - 2x3 + 3x = lim h - 0 10 f' h 5 = lim h - 0 h X -2 2 = lim h - 0 Video Example () (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)