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Answer the following questions about the function whose domain is ( - co,co) and whose derivative is f'(x) = x ( X - 3 ). a. Find the critical points, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) of f is/are x = (Simplify your answer. Use a comma to separate answers as needed.) O B. The function f has no critical points. b. Determine where f is increasing and decreasing. Select the correct choice below and fill in the answer box to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed.) O A. The function f is increasing on the open interval(s) , and decreasing on the open interval(s) O B. The function f is decreasing on the open interval(s) , and never increasing. O C. The function f is increasing on the open interval(s) , and never decreasing. c. Determine the local maximum/maxima, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function f has a local maximum at x = (Simplify your answer. Use a comma to separate answers as needed.) O B. There is no local maximum. Determine the local minimum/minima, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. There is no local minimum. O B. The function f has a local minimum at x = (Simplify your answer. Use a comma to separate answers as needed.)Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. r(x)=5e 'x, a = o.o1 Set the center of the linearization as x =D. Answer the following questions about the function whose derivative is f'(x) = (x - 3)2(x + 4). a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values? Identify the function's local extreme values, if any, saying where they occur. f ( x ) = ex + e -x . . . . . Fillu vacil local maxIIIIII, II ally. Select we Collect CIjuice welow allu, Imnecessary, IIII III we allswel boxes To CUTTipleLe youI CIJUICE. (Type exact answers.) O A. The function has a local maximum value at one value of x. The maximum value is f() =. O B. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are f () = and f( ) = O C. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are f( ) =, F ( ) =, and f( ) =. D. There are no local maxima. Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Type exact answers.) O A. The function has a local minimum value at three values of x. In increasing order of x-value, the minimum values are f() =, F( ) =, and f() = O B. The function has a local minimum value at two values of x. In increasing order of x-value, the minimum values are f() = and f ( ) = O C. The function has a local minimum value at one value of x. The minimum value is f ([ ]) = [. O D. There are no local minima.Find the absolute maximum and minimum values of the following function on the given interval. Then graph the function. Identify the points on the graph where the absolute extrema occur. ' 117: It f(B)sm0, - 6 5952 Find the absolute maximum. Select the correct choice below and. if necessary, ll in the answer boxes to complete your choice. 'VA' 31: The absolute maximum value 1 occurs at 6 = ? . (Use a comma to separate answers as needed. Type exact answers, using 1r. as needed.) B. There is no absolute maximum. Find the absolute minimum. Select the correct choice below and, if necessary. ll in the answer boxes to complete your choice. (Q A- The absolute minimum value |:| occurs at 6 = Cl. (Use a comma to separate answers as needed. Type exact answers, using 1: as needed.) O B. There is no absolute minimum