Question 62423: If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! If f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.
Find the places that the function = 0, this will tell us the intervals to test.
0=x(x+3)(x-1)
x=0 and x+3=0 and x-1=0
x=0 and x=-3 and x=1
The intervals are (-infinity,-3),(-3,0),(0,1), and (1,infinity)
For (-infinity,-3) test x=-4
-4(-4+3)(-4-1)>0 ?
-4(-1)(-5)>0 an odd number of negatives gives us a negative
-20>0 is false, so this interval is not part of the solution set.
:
For (-3,0), test x=-1
-1(-1+3)(-1-1)>0 ?
-1(2)(-2)>0 an even number o0f negatives is positve
4>0 is true, so (-3,0) is part of the solution set.
:
For (0,1) test x=1/2
1/2(1/2+3)(1/2-1)>0?
1/2(7/2)(-1/2)>0 an odd number of negatives gives a negative.
-7/8>0 is false, so this interval is not part of the solution.
:
For (1,infinity) test x=2
2(2+3)(2-1)>0?
2(5)(1)>0 no negatives make a postive
10>0 is true, so (1,infinity) is part of the solution.
:
Therefore the solution is: (-3,0)U(1,infinity)
Happy Calculating!!!
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