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Question 72717: I'm confused...help?
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.
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Find the values when f(x)=0
They are x=-1, or x=0, or x=4
Draw a number line and put the values -1,0,and 4 in proper order.
This determines 4 intervals; determines which intervals are part
of the solution set for f(x)>0 by choosing a test pt in each interval
and determining the sign of f(x)
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In (-inf,-1) choose x--100 where f(x)=-*-*- which is negative, so no solutions
In (-1,0) choose x=-1/2 where f(x)=-*+*- which is positive, so solutions here
In (0,4) choose x=2 where f(x)=+*+*- which is negative, so no solutions here
In (4,+inf) choose x=100 where f(x)=+*+*+ which is positive , so solutions here
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Therefore the solutions are in these intervals: (-1,0) union (4,+inf)
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Cheers,
Stan H.
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