3. Let f ( x ) = 3x 14 - x. 3 ( a) List the domain of f. Explain your reasoning. ( b ) Find the x- and y-intercepts of the graph (c) Find Rim f( x ) & lim f(x ) a use these to describe the end behavior * 7 - 00 x -+ 00 of the graph of f ( d ) . Find & simplify f' ( x ) ii. Make a Sign diagram for f (x). iii. Interpret your Sign Diagram for f'( x) in order determine the open intervals over which f is increasing decreasing: locations of any local maximums: (c, f (c) ) locations of any local minimums: (c, f ( c ) ) ( e) i. Find & simplify f" (x). ii. Make a Sign Digram for f"(x ). ill. Interpret your Sign Diagram for f" (x) in order to determine the open intervals over which f is. concave up . concave down. locations of any inflection points ( c , f (c ) ) ( f) Use your results from parts ( a) through (e) to sketch an incredibly detailed graph of y= f ( x ). Label the intercepts, local extrema, i inflection points