- #1
Felafel
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Homework Statement
Given the function "P" defined by: P(x) := x^2n + a2n-1*x^2n-1 + ... + a1x + a0;
prove that there exists an x* in |R such that P(x*) = inf{P(x) : x belongs to | R}
Also, prove that:
|P(x*)| = inf{|P(x)| : x belongs to |R}
The Attempt at a Solution
As the function is the sum of continuous functions, it is contnuos too.
Then, I thought about the theorem according to which if we have a cont. function on a sequentially compact space, it has inf. and sup. therein.
But the space here is not sequentially compact.
Can I use this theorem all the same, by adding some restrictions, perhaps?
thanksss