Question: 3) Consider the function f, whose formula and derivatives are given below: (40 pts) f (x) =-* f'(x) = =2x3-1 6x2(x3+2) ( x 3 -1)3

3) Consider the function f, whose formula and derivatives are given below: (40 pts) f (x) =-* f'(x) = =2x3-1 6x2(x3+2) ( x 3 -1)3 a) Find and describe all of the vertical, horizontal and slant asymptotes of this function, if any. b) Find all of the roots of this functions, if any. c) Find all of the local extrema of this function, if any. d) Find all of the infection points of this function, if any. e) Sketch this function, including all of the features above in your sketch

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