- #1
phoenixXL
- 49
- 3
Homework Statement
Suppose [itex]p(x)\ =\ a_0\ +\ a_1x\ +\ a_2x^2\ +\ ...\ + a_nx^n[/itex].
Now if [itex]|p(x)|\ <=\ |e^{x-1}\ -\ 1|[/itex] for all [itex]x\ >=\ 0[/itex] then
Prove [itex]|a_1\ +\ 2a_2\ +\ ...\ + na_n|\ <=\ 1[/itex].
2. Relevant Graph( [itex]|e^{x-1}\ -\ 1|[/itex] )
The Attempt at a Solution
From the graph we can conclude that
p(x) should pass through (1,0)
=> [itex]a_1\ +\ a_2\ +\ ...\ + a_n\ =\ 0[/itex]
Further, I'm not able to apply any other condition given to simplify the expression. Their is of course something to do with the derivative as I found this question in a book of differentiation.
Any help would be highly appreciated.
Thanks
Last edited: