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Question 64388: f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0?????
here is what I got so far.
x=0, x=-3, x=1
I'm not sure where to go from here??? Some of the answer for example have (-3,0)U(1,0)
?????
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0?????
here is what I got so far.
x=0, x=-3, x=1
I'm not sure where to go from here??? Some of the answer for example have
(-3,0)U(1,0)
Comment: That's not (1,0); it's (1,inf)
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You have found the values of x where f(x)=0
You need to find the intervals where f(x) is greater than 0.
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Draw a number line and mark the points -3,0,and 1.
This breaks the line into four intervals. You need to find
the interval(s) where f(x)=x(x-1)(x+3)>0
Interval I is (-inf,-3): pick the value x=-100 then f(-100)=(-)(-)(-)
which is negative; so no solutions in that interval.
Interval II is (-3,0): pick the value x=-1 then f(-1)=(-)(+)(-)
which is positive; so this interval is part of the solution
Interval III is (0,1): pick the value x=(1/2) then f(1/2)=(+)(+)(-)
which is negative; so no solutions in that interval
Interval IV is (1,inf): pick the value x=100 then f(100)=(+)(+)(+)
which is positive; so this interval is part of the solution
SOLUTION: (-3,0)U(1,inf)
Cheers,
Stan H.
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