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April 16, 2014

April 16, 2014

Posted by **FUNCTIONS** on Friday, July 5, 2013 at 2:07pm.

a) (x + 1)(x – 2)(x – 4)2 > 0

- advanced functions -
**MathMate**, Friday, July 5, 2013 at 3:03pmFrom 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 (x-2) 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,+∞)

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