Question

3.11 Theorem. Suppose f(x)-a"x" + an-lx"-+ + ao is a poly- nomial of degree n > 0 and suppose an > 0. Then there is an integer k such that ifx >k, then f(x)> 0. Note: We are only assuming that the leading coefficient an is greater than zero. The other coefficients may be positive or negative or zero. The next theorem extends the idea that polynomials get positive and roughly states that not only do they get positive, but th big from some point on. Notice that the theorem does not ask you to be efficient and find the first place after which the polynomial stays larger than some value. It just asks you to prove that eventually that happens. 3.12 Theorem. Suppose f(x)-an" +an-1"ao is a polyno- mial of degree n > 0 and suppose an > 0. Then for any number M there is an integer k ówhich depends on M) such that ifx > k, then f(x)> M

Answer 1

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