1. Find antiderivatives of each of the a) 5x1-3/x3 -5-2/x c) e+ sinx following: b) 3cos x +2secx d) 21#x-4h2-2013 2. A ball is thrown downwards from the top of a cliff 128 ft. above a river 3. Find the maximum and the minimum values of f(x)=x+4x on [13]. 4. Let g(x) 10 3x2 x3 with a velocity of-32 ft/sec. With what velocity will the ball hit the ground? a) Tell on which intervals g(x) is increasing and on which intervals g(x) is decreasing.O b) Tell on which intervals the graph of g is concave up and on which intervals it is concave down. c) Write the coordinates of all local extrema and points of inflection. [5] d) Draw the graph. Answer (a) or (b). If you wish to answer both for extra credit, please indicate which is the extra. Please show your work. a) The sum of twice one number and four times another number is 24. Find the 5. two numbers whose product is as large as possible. b) Find the point on the graph of y=x2 that is closest to the point (0,1) If 2ys_3x2y + 2x-8y = 8 a) Find dy/dx. b) write an equation of the line tangent to the graph at (-1,2). Find the area bounded by the graph of y=x2-4x, the x-axis, x=-1 and x= 1.