Math 0120Examination #1SampleName (Print) _______________________________________ .Signature ___________________________________________ Score .TA (Circle oneInstructions:1. Clearly print your name and sign your name in the space above.2. There are 8 problems, each worth the specified number of points, for a total of100 points. There is also an extra-credit problem worth up to 5 points.3. Please work each problem in the space provided. Extra space is available onthe back of each exam sheet. Clearly identify the problem for which the space isrequired when using the backs of sheets.4. Show all calculations and display answers clearly. Unjustified answers willreceive no credit.5. Write neatly and legibly. Cross out any work that you do not wish to beconsidered for grading.6. Calculators may not be used. All derivatives are to be found by learnedmethods of calculus.Arrington A________________________1. (8 pts.) f(x) =1x22and g(x) = .1x2(a) Find the domain of f.(b) Find the composition f(g(x)).2. (12 pts.) (a) Write the definition of the derivative of f(x).(b) Use the definition to find the derivative of f(x) = .x2Arrington A3. (5 pts.) A car traveling at a speed of v miles per hour should be able to come to a complete stopin a distance of D(v) feet. Interpret )50(D=6 (include units).4. (6 pts.) Give examples (no graphs) of:(a) A function f that is defined at x = 2, but discontinuous at x = 2 because ).2(f)x(flim2x(b) A function g that is continuous at x = -1, but not differentiable at x = -1 because of a sharpcorner at x = -1.5. (35 pts.) Find the indicated derivatives of the following functions (you need not simplify):(a) ).x(fFind.200x8exx4)x(f23(b) f(x) = (2x2–x)(5x-3–10x). Find ).x(f(c) f(x) = ).x(fFind.x11x32(d) f(x) = (3x5–18x)8. ).x(fFind(e) f(x) = )x(fFind.x201x3226. (12 pts.) At time t = 0, a diver jumps from a diving board that is 32 feet high. The height of the diverabove the water at t seconds is given byh(t) = -16t2+16t + 32 = -16(t2–t –2) feet.(a) Find the diver’s velocity at t = 0 seconds.(b) Find the diver’s acceleration at t = 1 seconds.(c) At what time will the diver hit the water?(d) What is the diver’s impact velocity?You may earn up to 5 points extra credit by finding the average velocity between t = 0 seconds and t = 1seconds.Arrington A7. (10 pts.) f(x) = x . Find the instantaneous rate of change of f at x = 1 and the equation of thetangent line at x=1 in point-slope form.8. (12 pts.) The revenue function for a certain commodity is given by R(x) = 3x 11x2thousand dollars, where x is the number of units sold. Find the marginal revenue, the averagerevenue and the marginal average revenue. Estimate the revenue generated by the 6-th