advanced functions

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Solve for x, x ϵ R
a) (x + 1)(x – 2)(x – 4)2 > 0

  • advanced functions -

    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 (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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