Arrington A Math 0120 c Examination #1 04-2 Name (Print) S.S.# . Signature Score . TA (Circle one) Andreou (12) Andreou (3) Ghebregiorgis Wajdowicz Instructions: 1. Clearly print your name and social security number and sign your name in the space above. 2. There are 9 problems, each worth the specified number of points, for a total of 100 points. There is also an extra-credit problem worth 10 points. 3. Please work each problem in the space provided. Extra space is available on the back of each exam sheet. Clearly identify the problem for which the space is required when using the backs of sheets. 4. Show all calculations and display answers clearly. Unjustified answers will receive no credit. 5. Write neatly and legibly. Cross out any work that you do not wish to be considered for grading. 6. Calculators may not be used. All derivatives are to be found by learned methods of calculus.Arrington A 1. (8 pts.) f(x) = 122−x and g(x) = 12−x . (a) Find the domain of f. (b) Find the composition f(g(x)). 2. (12 pts.) Use the definiton of derivative to find the derivative of f(x) = x2.Arrington A 3. (11 pts.) If total costs are given by and total revenues are given by 361022)( ++= xxxC , both in dollars, where x is the number of units, 2250)( xxxR −=(a) Find the break-even points. (b) Find the value of x which maximizes the profit and the maximum profit. 4. (8 pts.) Give examples of: (a) A function f which is defined at x = 1, but discontinuous at x = 1. (b) A function g which is continuous at x = 2, but not differentiable at x = 2.Arrington A 5. (30 pts.) Find the derivatives of the following functions (you need not simplify): (a) π2002834)( +−−+= xexxxf . (b) )1035)(22()( xxxxxf −−−= (c) 3112)(xxxf−+= (d) 8)1853()( xxxf −= (e) 332012)(⎟⎟⎠⎞⎜⎜⎝⎛+−=xxxxfArrington A 6. (8 pts.) At time t = 0, a diver jumps from a diving board that is 32 feet high. The height of the diver above the water at t seconds is given by feet. )22(163216216)( −−−=++−= ttttth (a) Find the diver’s velocity at t = 0. (b) Find the diver’s acceleration at t = 3. (10 pts) Extra-Credit Problem: (a) At what time will the diver hit the water? (b) What is the diver’s velocity at impact?Arrington A 7. (8 pts.) xxf =)(. Find the slope of the tangent line at x = 9 and the rate of change of f at x = 1. 8. (10 pts.) The revenue function is given as =)(XR 900024 +xx dollars where x is the number of units sold. Find the marginal revenue, the average revenue, and the marginal average revenue. 9. (5 pts.) A car traveling at a speed of v miles per hour should be able to come to a complete stop in a distance of feet. Interpret , including units.