231 TEST 3You may use your notebook during the last half hour of this exam.You may NOT use calculators, cell phones, loose papers, or peeking.Math 231April 7, 2011 . Name:By printing my name I pledge to uphold the honor code.All problems on this exam are multiple choice. You do NOT need to show your work.Figure things out on the scrap page and write only your final answers here. Please circleonly ONE answer for each problem.1. Find the x-value of the infl ection point of the function f (x) = x(x − 1)(x − 3).13143532 32. Find the x-value at which the derivative of f (x) =√x − 2x is zero. You may assumethat x ≥ 0.011614121√213. Find the local maximum of the function f (x) =(x−1)2x+2.−7 −5 −3 −1 0 14. Find the global maximum of the function f (x) = x√x2+ 1 on the interval [0, 4].Indicate which are global minima and wh ich are global maxima.0 1 1.5 2 3 45. The graph of the implicit function y3− 9y − x2= 0 has a horizontal tangent line atthree coordinate points (x, y). Only one of these points is in the list below; circle it.(0, 1) (1, 0) (0, 2) (2, 0) (0, 3) (3, 0)6. What is the x-value at which the function f (x) = x3−9x2+18x satisfies the conclusionof Rolle’s Theorem on the interval [3, 6]?0 3 6 3 +√3 3 −√31437. What is the value x = c at which the function f (x) = x2−6x+8 satisfies the conclusionof the Mean Value Theorem on the interval [0, 4]?−1 0 1 1.5 2 2.58. Suppose you are on a planet whose gravity causes a falling object to have a downwardacceleration of a(t) = −40 feet per second per second. Given that an object has initialposition 100 feet from the ground and an initial velocity of 0 feet per second, find anequation for its position s(t) after t seconds.−10t+100 −20t+100 −40t+100 −10t2+100 −20t2+100 −40t2+1009. Find the length, in feet, of the long side of the largest rectangular chicken pen thatcan be fenced off with total of 1200 feet of fencing material if a straight river is usedfor one side of the pen.250 300 400 500 600 80010. Suppose a cone is changing shape in such a way that its height is always two-thirds ofits radius. If th e radius of the cone grows at a rate of 4 inches per second, how fast,in inches per second, is the volume of the cone changing when the radius is 3 inches?6π 12π 24π 36π 48π 72πSurvey for 2 bonus points: How do you think you did? What is a question or topic thatcould have been on this exam, but