Find the intervals on which f is increasing and decreasing. 2 f(x)= -2x +16|nx (:> Select the correct choice below and, if necessary, ll in the answer box(es) within your choice. A- The function is increasing on the open interval(s) and decreasing on the open interval(s) (Simplify your answers. Type your answers in interval notation. Use a comma to separate answers as needed.) B- The function is decreasing on the open interval(s) . The function is never increasing. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) '3"? C. The function is increasing on the open interval(s) . The function is never decreasing. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) D. The function is never increasing or decreasing. Find the intervals on which fis increasing and decreasing. f(x) = 3 cos 2x on [- run] (3 Select the correct choice below and, if necessary, ll in the answer box(es) within your choice. ":9 A- The function is increasing on the open interval(s) and decreasing on the open interval(s) (Simplify your answers. Type your answers in interval notation. Type exact answers, using 11: as needed. Use a comma to separate answers as needed.) "'3' B- The function is decreasing on the open interval(s) . The function is never increasing. (Simplify your answer. Type your answer in interval notation. Type exact answers. using 1: as needed. Use a comma to separate answers as needed.) C. The function is increasing on the open interval(s) . The function is never decreasing. (Simplify your answer. Type your answer in interval notation. Type exact answers, using it as needed. Use a comma to separate answers as needed.) "'21- D. The function is never increasing or decreasing. Complete parts a through c for the given function. f(x)= -3x2+x+2; [4,4] 1 The critical point(s) is(are) at X: E . (Simplify your answer. Use a comma to separate answers as needed.) The function does not have a critical point. b. Use the First Derivative Test to locate the local maximum and minimum values. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Use a comma to separate answers as needed.) " 1 The local maximum/maxima is/are at X: E . The local minimum/minima is/are at x= and the local maximum/maxima is/are at x= The local minimum/minima is/are at x = There is no local minimum and there is no local maximum. (2. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Simplify your answer. Use a comma to separate answers as needed.) ii? A- The absolute maximum is atx= and the absolute minimum is atx= '33:? B- The absolute minimum is at x= , but there is no absolute maximum. Perform a rst derivative test on the function f(x) = x 25 x2 ; [- 5,5]. 3. Locate the critical points of the given function. b. Use the first derivative test to locate the local maximum and minimum values. c. Identify the absolute minimum and maximum values of the function on the given interval (when they exist). E) 3. Locate the critical points of the given function. Select the correct choice below and, if necessary, ll in the answer box within your choice. ":3? A- The critical p0int(s) are located at x= (Use a comma to separate answers as needed.) {:1- B. There are no critical points. A theorem states that iffis continuous on an interval I that contains one local extremum at c and if a local minimum occurs at c, then f(c) is the absolute minimum offon I, and if a local maximum occurs at c, then f(c) is the absolute maximum of f on |. Verify that the following function satises the conditions of this theorem on its domain. Then, nd the location and value of the absolute extremum guaranteed by the theorem. f(x)=xe "\"3 The function f(x) = x e _X/3 has an absolute extremum of at X: (Type exact answers.)