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1Solutions to “Functions and graphs”1. Find the intervals on whichf(x) =x(x-1)(x+ 1)is positive, andthe intervals on which it is negative.2. Find the intervals on whichf(x) = (3x-2)(x-1)(x+1)is positive,
and the intervals on which it is negative.Solution:Same method as the last question.The functionf(x)is zero precisely whenx=-1,23,1.Therefore on each interval(-∞,-1),(-1,23),(23,1),(1,)its sign is constant, but the signchanges from one interval to the next. Whenx= 100we see thatf(x)>0, so we conclude thatf(x)is positive on the second andfourth intervals and negative on the first and third:f(x)negative

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