advanced functions
posted by FUNCTIONS on .
Solve for x, x ϵ R
a) (x + 1)(x – 2)(x – 4)2 > 0

From the function:
f(x) = (x + 1)(x – 2)(x – 4)²
we see that it is a quartic with leading coefficient equal to 1. So the shape of the curve is like a letter W.
Since factors (x+1) and (x2) are distinct, we see that f(x)<0 ∀ xϵ(1,2).
The double root at x=4 means that f(4)=0.
Thus f(x)>0 ∀xϵ (∞,1)∪(2,4)∪(4,+∞)