X ek 6-7 Week 6-7 (ULOb) Let's Check Activity (ULOb) Let's Analyze Activity (answer 1 item only) 4. A searchlight is trained on the side of a tall building. As the 1. In each part, determine f'(x). light rotates, the spot it illuminates moves up and down the (a) f(x) = 16 (b) f (x) = Vox side of the building. That is, the distance D between ground (c) f(x) = 6,x (d) f(x) = vox level and the illuminated spot on the side of the building is a function of the angle @ formed by the light beam and the 2. In parts (a) (d), determine f'(x). (b) f (x ) = x (x) + 5) horizontal (see the accompanying figure). If the searchlight (a) f(x) = x +5 is located 50 m from the building, find the rate at which D (c) f (x ) = - *+5 x3 + 5 is changing with respect to @ when 0 = 45. Express your 2 (d) f ( x ) = answer in units of meters/ degree. 4. If f(x) = 3x3 - 3x2 + x + 1. then f"(.x) = _ 10. Find dy/dx. (a) y = sin x (b) y = cosx (c) y = tan x (d) y = sec x 17. Find dy/dx. (a) y = sin(3.x + 2) (b) y = (x2 tan.x)4 50 m