Select Page

1.If y = x3 + 2x and , find when x = 2. Give only the numerical answer. For example, if = 3, type only 3. ( 4 points) 2.The area A = πr2 of a circular water ripple changes with the radius. At what rate does the area change with respect to the radius when r = 4ft? (4 points)16π ft2/ft8π ft2/ft8 ft2/ft4π ft2/ft3.A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h cm3. Find the rate at which the volume of the box is changing when the edge length of the base is 4 cm, the edge length of the base is increasing at a rate of 2 cm/min, the height of the box is 15 cm, and the height is decreasing at a rate of 3 cm/min. (4 points)The volume of the box is decreasing at a rate of 192 cm3/min.The volume of the box is increasing at a rate of 288 cm3/min.The volume of the box is decreasing at a rate of 288 cm3/min.The volume of the box is increasing at a rate of 192 cm3/min.4.The height of a cylinder with a fixed radius of 4 cm is increasing at the rate of 2 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 14cm. (4 points)16π28π32πNone of these5.A 10-ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/sec, how fast, in ft/sec, is the top of the ladder sliding down the wall, at the instant when the bottom of the ladder is 6 ft from the wall? Answer with 2 decimal places. Type your answer in the space below. If your answer is a number less than 1, place a leading “0” before the decimal point (ex: 0.35). (4 points)