I have to prove that: f(x)=P(x)+P′(x)+P"(x)+......+Pn(x)>=0 for all x.

ahredent89

ahredent89

Answered question

2022-08-11

I have to prove that:
f ( x ) = P ( x ) + P ( x ) + P " ( x ) + . . . . . . + P n ( x ) 0 for all x

Answer & Explanation

Trevor Copeland

Trevor Copeland

Beginner2022-08-12Added 21 answers

you can let
G ( x ) = f ( x ) e x , < x <
then we have
G ( x ) = f ( x ) e x f ( x ) e x = P ( x ) e x 0
so this G ( x ) is decreasing and
lim x + G ( x ) = lim x + f ( x ) e x = 0
f ( x ) e x = G ( x ) lim x + G ( x ) = 0
so
f ( x ) 0

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