1.) If f(2) = 3 and f'(2) = -1, find the equation 2.) Find the equation of the tangent line to the graph of the tangent line when x = 2. of f (x) = x2 -2x -3 when x=2. (2, - 3) lim f ( 2 ) = ( 25 - 2(2)-3 4- 4- 3 f ( 2 ) = - 3 - 2 y + 3= 2( X- 2) f' ( * * ) = 2 x - 2 y + 3: 2x-4 f ' ( 2 ) = 2 (2 ) - 2 y= 2x- 7 3.) Differentiate y = - 3x x 2 + 1 f( xth ) - f ( x ) 4.) For the function f (t) = - 1 + 2, find the following. h y= 3x+ x+1-3x a.) the average rate of change of f (t) on the -00.9 we war interval [1, 4] (24)" To oulov ardi stemitall (d | do grinsom b.) the instantaneous rate of change of f (t) when t = 2 5.) Suppose that h(x) = 8(x) and 2 ( - 2 + Ax ) - 2 ( - 2 +4x ) - 2 - (-14 ) f (x) 6.) lim Ar -+ 0 g (2) = 3, 8'(2) = -1, f(2) = 5, f'(2) =-2. Ax Find h'(2). represents f' (c) for a function f (x) and a number c . Find f (x) and c. 62: (A)7.) Let h(x) = f(x).8(x). 6 /V Find h'(2). (-1,5) vof (x) (A) -2 (B) 1 (3,1) (6, 3) (C) 7 (D) -1 8.) What is g'(3) ? (3,-1) (7,-4 ) (1,-5) 9.) One lazy day, Uncle Si decides to sit under a shade tree next to a road by the swamp and count the number of ducks which cross the road. The data in the table below shows the accumulation of the number of ducks crossing this road at each hour after 9:00am. Hours after 9AM 0 2 3 3 4 5 6 7 # of ducks that have crossed the road 3 8 11 12 21 24 28 Find the following: a.) Determine the average number of ducks which | b.) Estimate the value of f' (4.5) and explain its have crossed the road per hour during Uncle Si's 7-hour observation. Label your result. meaning. 10.) The graph of f' , the derivative of f, is shown for -2