The distance an object falls (when released from rest, under the inuence of Earth's gravity, and with no air resistance) is given by d(t)=16t2, where d is measured in feet and t is measured in seconds. A rock climber sits on a ledge on a vertical wall and carefully observes the time it lakes for a small stone to fall from the ledge to the ground, 3. Compute d'(t). What units are associated with the derivative. and what does it measure? b. If it takes 4.4 s for a stone to fall to the ground, how high is the ledge? How fast is the stone moving when it strikes the ground (in miles per hour)? a. d'(t) = The units associated with the derivative are V and it measures the E of the stone. b. The ledge is feet high. (Round to the nearest integer as needed.) The stone is moving at mi/hr when it strikes the ground. (Round to the nearest integer as needed.) Find the derivative of the following function by rst expanding the expression. f(x) = (3x + 1) (5x2 + 4) f'(x) = D Let G = 2f - g, where the graphs of f and g are shown in the figure to the right. Find the following derivative. G'(3) LX CO - G'(3) =U56 the graph 0\" in the gure 10 do the fOHOWihQ- a. In the interval (0,5), f is not continuous at x = 3. Find the values of x in the interval (0,5) at which f is not continuous. (Use a comma to separate answers as needed.) b. Find the values of x in the interval (0,5) at which f is not differentiable. c. Sketch a graph of f'. b. In the interval (0,5), fis not differentiable at x = (Use a comma to separate answers as needed.) Ay a 10 c. Choose the correct graph below. 8 e 0' C) A. 4 2' y 2.7 >Ki D 10 0' X 0 > _2 1 ? 3 4 5 .4 .5 _1 -8 -1 O c V