Question 65470: 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! f(x)=x(x+3)(x-1) use interval notation to give all values of x where f(x)>0
f(x)=0 when:
x=0 or x+3=0 or x-1=0
x=0 or x=-3 or x=1
Therefore, the intervals to test are:
(-infinity,-3) or (-3,0) or (0,1) or (1,infinity)
For (-infinity,-3) test -4:
f(-4)=-4(-4+3)(-4-1)=-4(-1)(-5)=-20 <--negative, reject this interval
For (-3,0) test -1:
f(-1)=-1(-1+3)(-1-1)=-1(2)(-2)=4 <--positive, accept this interval
For (0,1) test .5
f(.5)=.5(.5+3)(.5-1)=.5(3.5)(-.5) -.875 <--negative reject this interval
For (1, infinity) test 2:
f(2)=2(2+3)(2-1)=2(5)(1)=10 <--positive, accept this interval
Therefore your solution is:
(-3,0)U(1,infinity)
Happy Calculating!!!
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