2. The purpose of this problem is to show pretty much all of our rules at work at once. If f(x) = sin vita , find fr(x). sin 2 -resin 323 (1+3)? O sin ' -2'sin o'+4r ain cocos al 'sin'r' + 4x'sin ax-cos a' (1+13)2 O sin a' -a'sin 'n' + 4x sin r-cos aUse implicit differentiation to find the slope of the tangent line to the curve -_ =x - 6 at the point (1, O 23 289 O 44 289 O 63 34 O 54 289. Evaluate the limit using I'II-4;pitnl's rule. 11m 38.\". 7 n . Find ff(.1;). Emll (2.: * M165 ,1} lu'lu' (2x - H35 1) D D . Consider the Function u!) = 5:121 7 41: on the interval [74, 4]. Find the average or mean slope m of this mction on this interval. By the Mean Value Theorem. we know there exist-s at. least. one c in the open interval (74, 4-) such that [c) is equal to this mean slope. For this problem, there are two value:- ofc that work. Find the two values ofc in the interval which. works. 3 m = 32...: = 2.31 or 2.31 D m = 76.1 = 1.55 or 1.55 D m = 321;: = 1.55 or 1.55 D m : 76.5 : 2.31 or 2.31 Let f(2) = sin +cos :' . Find fi(2x). 8 + 167 8 + 85 8 - 87 8 - 167 Let |x|