Let f be the function defined by f(x): 1-2x² x²-1 (a) Determine the vertical and horizontal asymptotes (show all limits). (b) Use the sign pattern for f'(x) to determine (i) the interval(s) over which f rises and where it falls; (ii) the local extrema. (c) Use the sign pattern for f" to determine (i) where the graph of f is concave up and where it is concave down. (ii) the inflection points (if any)

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