Question 1)

lfa function f{m] is continuous on [5,15] and ditTerentiable on (a, b), then the Mean Value Theorem says that there is at least one number c in the interval (a, 5] such that f'[c) = y. Find all possible value(3} for a given f(z] : m3 3m + 5, 2 g a: g 2. Enter your answer(s) separated by commas. Atelewsion camera is DOSITlOFIed 4000 ft from the base of a rocket launching pad. The angle of elevation Of the camera has to change at the conect rate in order to keep the rocket In Sight. N50, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Let's assume the rocket rises vertically and its speed is 600 fit/s when it has men 3000 ft, (a) How fast is the distance from the television camera to the rocket changing at that moment? (ti) It the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at that same moment? (a) 350 (b) A street light is at the top of a 10 [out tali pole, A6 foot tall woman walks away from the pole with a speed 0M msec along a siiaighl path How fast is the tip of her shadow moving when she is 40 feel from the base of the pole? The tip of the shadow iS moving at