1. Differentiate each of the following. Do not simplify your answer. a) y=7 b) g(x) = 5x4 - 3 x-5 4x-12 c) f( x) = 3 d) f(x) = (8x3 - 4x) (3x2 + x) 1 e)h(x) = (6x2 - 4x)5 f) g(x) = 8x2 - 6 1 5x5 - 7 d) m(x) = (8x - 9)3 (6x4 - 2x)7 h) y = (5x + 6)V4 - x22. Prove that the following is a derivative rule. Justify your answer with an example. 0 jxiflx) + gm] = rm + gtxl 3. Given v = (2x + 1)3 (3x 5j5 ' a] Determine the derivative and then write your answer in simplied form. b) Determine the value(s) of x for which the graph of x) has a horizontal tangent. \f5. For the equation v = 2(4x3 - 5F, predict with a formula, - a] The derivative that first becomes a constant and the 6'\" derivative value. b} The value of the 8'\" derivative. 6. Given the position versus time graph determine - a) When the object stationarv? b) When the object's velocity positive? 7} The tangent line to the curve defined by x] = x3 6x2 + 8x at the point (3, -3}, intersects the curve at another point B. Find the coordinates of B. u 8) Determine the equation of the tangent line to the graph of y = -x2 + 9x -1, where the slope of the tangent is 5.91 The position of an object moving long a straight line can be modeled by the function sit} = 3t3 4D.5 t2 + 1|?thr where sis the position in meters att seconds andtz 0. - 3} Determine the velocity and acceleration function for the object. bJDetermine the position of the object when the velocity is ll c} when does the object move to the left? d} Is the object moving toward or away from its starting position when t =4? Explain