Question 107005: If f(x) = x(x + 1)(x – 4), use interval notation to give all
values of x where f(x) > 0.
a. (–1, 4)
b. (–1, 0) ∪ (4, ∞)
c. (–1, 4)
d. (0, 1) ∪ (4, ∞)
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! 
Let's look at the key x values and determine the sign of f(x).
At x=0, f(x)=0
That knocks out a and c because they include x=0 (they're the same answer?).
Since both b and d include x>4, we won't look at that.
Anyways when x>4, f(x)>0 because x>0, x+1>0, and x-4>0.
The two other regions to choose are (-1,0) and (0,1).
b.)If you choose a point between (-1,0), say x=-1/2, then
x<0, because -1/2<0.
x+1>0, because -1/2+1=1/2>0
x-4<0.
The product would then be negative times positive times negative.
The product (f(x)) would be positive.
d.)If you choose a point between (0,1), say x=1/2, then
x>0, because 1/2>0.
x+1>0, because 1/2+1=1/2>0
x-4<0.
The product would then be positive times positive times negative.
The product (f(x)) would be negative.
The answer is b.
b. (–1, 0) ∪ (4, ∞)
|
|
|
