uiz __4__ Math 140 Calculus I Name _______________ Ms. Chowdhury Fall 2016 Date ____________________ INSTRUCTIONS The quiz is worth 40 points. Each of the 10 questions is worth 4 points 1.)This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. 2.) You must show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit at the discretion of the professor.Showing work for the other questions is not mandatory, but recommended so that if needed I can see where your mistakes were made. 3.) Please type or handwrite your answers on the provided answer sheet. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. 4.) Finally, be sure to sign the honor statement. Without this your quiz may be invalidated. If you have any questions, please contact me by e-mail. Answer the question. 1) A trucker handed in a ticket at a toll booth showing that in 2 hours he had covered 214 miles on a toll road with speed limit 65 mph. The trucker was cited for speeding. Why? Approximate the root by using a linearization centered at an appropriate nearby number. 2) 147 Use the Second Derivative Test to find the local extrema for the function. 3) f(x) = x3 + 12x2 + 48x - 4 Solve the problem. 4) A container is the shape of an inverted right circular cone has a radius of 1.00 inches at the top and a height of 5.00 inches. At the instant when the water in the container is 1.00 inches deep, the surface level is falling at the rate of -2.00 in./s. Find the rate at which water is being drained. 5) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 5 m2 /s, how fast are the people moving when they are 5 m from the right angle? (Round approximations to two decimal places.) Find the points of inflection. 6) y = x3 + 12x2 - x - 24 1 Use the Concavity Test to find the intervals where the graph of the function is concave up. 7) y = -3x2 + 18x + 4 Solve the problem. 8) A ladder is slipping down a vertical wall. If the ladder is 20 ft long and the top of it is slipping at the constant rate of 2 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 16 ft from the wall? At the given point, find the slope of the curve and the line that is normal to the curve, as requested. 9) x2 - y2 = 17, normal at (-9, 8) Sketch a graph of a single function that has these properties. 10) a) Continuous and differentiable for all real numbers b) f (x) > 0 on (-3 , -1) and ( 2 , ) c) f (x) < 0 on (- , -3) and ( -1 , 2) d) f (x) > 0 on (- , -2) and ( 1 , ) e) f (x) < 0 on (-2 , 1) f) f (-3) = f (-1) = f (2) = 0 g) f (x) = 0 at (-2 , 0) and (1, 1) 2