Question 71928: If f(x)=x(x+1)(x-4), use interval notation to give all values of x where f(x)>0.
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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.
f(x) is zero if x=0 or x=-1 or x=4
Mark those values on a number line.
Those three numbers result in four intervals on the number line.
Find the intervals where f(x) is positive or >0 by picking a test value
and substituting that for x in f(x). Note only the sign of the answer.
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Interval (-inf,-1): Pick x=-100; you get f(-100)= -*-*- which is <0
Interval (-1,0) : Pick x=-1/2; you get f(-1/2)= -*+*- which is >0
Interval (0,4) : Pick x=2 ; you get f(2) = +*+*_ which is <0
Interval (4,inf) : Pick x=100 ; you get f(100)= +*+*+ which is >0
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So the solution is: (-1,0) or (4,inf)
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Cheers,
Stan H.
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