SOLUTION: If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0

Question 65471: If f(x)=x(x-1)(x-4)^2, 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-1)(x-4)^2, use interval notation to give all values of x where f(x)>0
f(x)=0 at
x=0 and x-1=0 and x-4=0
x=0 and x=1 and x=4
These are the end points (critical numbers) for your intervals to test:
(-infinity,0) or (0,1) or (1,4) or (4,infinity)
For (-infinity, 0) test a number less than 0 and see if it gives a positive answer. I'm using x=-1:
f(-1)=(-1)(-1-1)(-1-4)^2=-1(-2)(-5)^2=50 <--positive we want this
For (0,1), test x=.5
f(.5)=(.5)(.5-1)(.5-4)^2=.5(-.5)(-3.5)^2=-3.0625 <--negative we reject this
For (1,4), test 2:
f(2)=2(2-1)(2-4)^2=2(1)(-2)^2=8 <---positive we want this
For (4,infinity), test 5:
f(5)=(5)(5-1)(5-4)^2=5(3)(1)^2=20 <---positive we want this
Therefore the solution is:
(-infinity,0)U(1,4)U(4,infinity)
Happy Calculating!!!

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