Question 73963: IF f(x)=x(x+1)(x-4), USE INTERVAL NOTATION TO GIVE ALL VALUES OF x WHERE f(x)>0.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! IF f(x)=x(x+1)(x-4), USE INTERVAL NOTATION TO GIVE ALL VALUES OF x WHERE f(x)>0.
Mark x=0, x=-1, and x=4 on a number line forming intervals (-inf,-1), (-1,0),
(0,4)., (4,inf)
Check a test value in each interval to see which interval(s) are in the solution set.
Check x=-100; then f(x)=(-)(-)(-)<0 so no solution in (-inf,-1)
Check x=-1/2; then f(x)=(-)(+)(-)>0 so (-1,0) is part of the solution set.
Check x = 2 ; then f(x)=(+)(+)(-)<0 so no solutions in (0,4);
Check x=100; then f(x)=(+)(+)(+)>0 so (4,inf) is part of the solution set.
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Solution in interval notation: (-1,0) or (4,inf)
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Cheers,
Stan H.
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