Question 64426: if f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0???
I came up with x=0, x=1, x=4 but don't know how to proceed from here
Answer by stanbon(75887)   (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???
I came up with x=0, x=1, x=4 but don't know how to proceed from here
You have found the x-values that make f(x) equal zero.
Draw a number line; label point x=0, x=1, x=4
This breaks the line into four intervals where f(x) might be greater zero.
You need to check a value in each of these intervals:
If x=-100, f(-100)= -(-)(-)^2=positive so the interval (-inf,0) is part of the solution.
If x=1/2, f(1/2)=+(-)(-)^2<0 so (0,1) is not part of the solution
If x=3, f(3)=+(+)(-)^2>0 of (1,4) is part of the solution
If x=100, f(100)=+(+)(+)^2>0 so (4,inf) is part of the solution.
SOLUTION: (-inf,0) U (1,4) U (4,inf)
Cheers,
Stan H.
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