Use the rst derivative test to determine the location of each local extremum and the value of the function at this extremum. f(x} = 3x a? ' 4" Identify the location and function value of the maximum of the function, if any. Select the correct answer below and, if necessary, ll in any answer boxes within your choice. O A- The function has a local maximum of at x = (Use a comma to separate answers as needed. Type exact answers in simplied form.) O B. The function does not have a local maximum. Identify the location and function value ofthe minimum of the function, if any. Select the correct answer below and, if necessary, fill in any answer boxes within your choice. 0 A- The function has a local minimum of D at x = D. (Use a comma to separate answers as needed. Type exact answers in simplied form.) 0 B. The function GOES I101 have a local minimum. Evaluate the definite integral. 12(In x) dx X 12(In x) dx = 1 X (Round to three decimal places as needed. )Find all critical numbers of the function f{x) = (x (3)9. Then use the secondderivative test on each cn'tical numberto determine whether it leads to a local maximum or minimum. Select the correct choice below and. if necessary, ll in the answer ooxtes) to complete your choice. O A- The critical number(s) isr'are at x = . There is no local maximum. There is a local minimum at x = |:. (Type integers or simplied fractions. Use a comma to separate answers as needed.) O 3- The critical numberfs) isr'are at x = . There is no local maximum and no local minimum. (Type an integer or a simplied fraction. Use a comma to separate answers as needed.) O C. The critical number(s) israre at X = . There is a local maximum at X = |:. There is a local minimum at X = (Type integers or Simplied fractions. USE a comma [0 Separate answers as needed.) O '1 The critical numberfs) isr'are at x = . There is a local maximum at x= El. There is no local minimum. (Type integers or simplied fractions. Use a comma to separate answers as needed.) 0 E. There are no critical numbers