MATH 1401 UNIFORM FINAL EXAM MAY 8, 1999

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INSTRUCTIONS: READ THE PROBLEMS CAREFULLY. IF YOU DO NOT UNDERSTAND A QUESTION, ASK FOR CLARIFICATION. YOU HAVE 3 HOURS TO COMPLETE THE EXAM. YOU MAY USE AN 8.5X11 INCH CHEAT SHEET ANDA CALCULATOR. TO RECEIVE PARTIAL CREDIT, YOU MUST SHOW ALL WORK. THE MAXIMUM SCORE FOR THIS EXAM IS 100 POINTS: 50 POINTS FOR PART 1 AND 50 POINTS FOR PART 2. GOOD LUCK!





  1. Evaluate tex2html_wrap_inline156 .
  2. If tex2html_wrap_inline158 , evaluate tex2html_wrap_inline160 .
  3. Evaluate tex2html_wrap_inline162 .

    4. For Questions 4 and 5, consider the function

  4. Evaluate .
  5. When a = 4, is f continuous at x = 2?


  6. For what values of x is tex2html_wrap_inline174 differentiable?
  7. True or false: If a function is continuous at a point C then it is differentiable at C.


  8. True or False: The third derivative represents the rate of change of the second derivative.


  9. True or False: If f ' (x) = g ' (x) +c then f '' (x) =g '' (x).


  10. True or False: If f is a second degree polynomial, then f ''' (x) = 0.


  11. Evaluate f ' (x) when tex2html_wrap_inline190 .


  12. Find if tex2html_wrap_inline194 .
  13. Suppose we wish to find the absolute extrema of a function f defined on a closed interval [a,b] and that f'(c) = 0 where a < c <b. At what values of x might f have absolute extrema?


    14. Use the graph of f (below) on the interval [a,b] for problems 14 - 16.

  14. Find all values of x at which f / (x) = 0


  15. Find all intervals on the x-axis where f / (x) > 0


  16. Find all intervals on the x-axis where f // (x) > 0


  17. Evaluate tex2html_wrap_inline224 .


  18. Evaluate tex2html_wrap_inline226 .


  19. Give all functions f for which tex2html_wrap_inline230 .


  20. Evaluate tex2html_wrap_inline232 .


  21. Evaluate tex2html_wrap_inline234 .

  22. Evaluate tex2html_wrap_inline236 .


  23. Evaluate tex2html_wrap_inline238 .


    24. For problems 24-25, consider the graph of f shown in the graph below. Region A has an area of 2 square units and region B has an area of 4 square units. Find the value of the following integrals.



  24. tex2html_wrap_inline242 .


  25. tex2html_wrap_inline244 .




    1. Find dy/dx if tex2html_wrap_inline248 . Do not simplify.


    2. Find dy/dx if tex2html_wrap_inline252 (Use logarithmic differentiation).


  27. Find the equation of the line tangent to the curve at the point (-1,1).


  28. A spherical balloon is being inflated at the rate of 20 cubic feet per minute. How fast is the surface area of the balloon increasing when the radius is 4 ft. The surface area of a sphere is given by tex2html_wrap_inline258 . the volume of a sphere is given by tex2html_wrap_inline260 .


  29. Find the coordinates of all relative extrema (maxima and minima) and points of inflection of the function tex2html_wrap_inline262 .


    1. Evaluate the integral tex2html_wrap_inline264


    2. Evaluate the integral tex2html_wrap_inline266

Roxanne Byrne
Fri May 14 12:30:31 Mdt 1999