Find the derivative. 1) f(x) = 8 _3 6 ~x x x4' find f(x) A ) 4 3 24 B) -4 x + 3_ 24 4 3 24 4 x1/2 2 x2 x3/2 D) - - 24 2 x3/2 x2 5 Find an equation for the tangent to the curve at the given point. 2) y =x2 - x, (-3, 12) A)y =-7x+9 B) y=-7x - 9 C) y =-7x - 6 D) y =-7x +6 Provide an appropriate response. 3) Find all points (x, y) on the graph of f(x) = 2x2 -3x with tangent lines parallel to the line y =9x + 9. A) (6, 9) B) (3, 9) C) (0, 0), (3, 9) D) (3, 18) Find the derivative of the function. 4) y = = x3 x - 1 A)y' _ 2x3 - 3x2 B) y' _ 2x3 + 3x2 Cy's-2x3 + 3x2 D) y'=-2x3 - 3x2 (x - 1)2 (x - 1)2 (x - 1)2 (x - 1)2 The function s = f(0) gives the position of a body moving on a coordinate line, with s in meters and t in seconds. 5) s =613 + 812 +5, -3st=-1 Find the body's average velocity for the given time interval. A) 46 m/sec B) 3.5 m/sec C) -92 m/sec D) -7 m/sec 6) s = - 13 + 812 - 8t, Ost=8 Find the body's velocity and acceleration at the end of the time interval. A) 8 m/sec, 0 m/sec2 B) -72 m/sec, -8 m/sec2 C) 72 m/sec, -32 m/sec- D) -72 m/sec, -32 m/sec2 Solve the problem. 7) A ball dropped from the top of a building has a height of s =576 - 1612 meters after t seconds. How long does it take the ball to reach the ground? What is the ball's velocity at the moment of impact? A) 36 sec, -1152 m/sec B) 6 sec, -192 m/sec C) 6 sec, 192 m/sec D) 12 sec, -96 m/sec Find the derivative. 8) s = t+ tan t - t A) 45 = 14 sec t tan t + 413 tan t -1 21/t B) at ds =14 sec2 t + 413 tant - 1 2Vt ds =413 sec2 t -- C) at D) 95 = - 14 sec2 t + 413 tan t + = Find Dxy. 9) y = (4x5 - 4x4 + 7)300 A) 300(4x5 - 4x4 + 7)299 B) 300(4x5 - 4x4 + 7)2(20x4 - 16x3) C) 300(20x4 - 16x3, 299 D) 300(4x5 - 4x4 + 7)29(5 x4 - 4x3)\f