The Secret presidential function, w/ f'(0) = 1, f"(0) = 1, f'''(0) = 1.

[AquaMan]

[SIZE=+3]The Secret Presidential Function
[/SIZE]
President Clinton derives all his mystical power from a secret power function. This function is so secret that no one person knows all its values. Vice President Gore, knows all about the function at x = 1. His running mate, Joe Lieberman, knows all about the function at x = 0.9. In a silent auction, an in-the-closet democrat and classmate Mr. Strickland bought the information about x = 0.8, and so on. Thus, if Gore could only find f(1), he could win the election and run the whole show!

So we get Bush Jr. to talk. He is angry, because he knows about the function at x = 0 and believes that is enough to make him President -- but it is not enough. He knows that \(\displaystyle f(0)\, =\, 1,\, f'(0)\, =\, 1,\, f^{'''}(0)\, =\, 1,\) and so forth. "Wow," we say, "Your dad trusted you with a really big secret!"

"What are you talking about?" Bush Jr. complains. "Yeah, I know a lot about the function, but just at the measly point x = 0! I know nothing about f(1), which is what I need to steal the election from Gore! Erm... not that I would want to, of course. Heh, heh, ahem."

We dismiss Bush Jr., and he goes back to his ranch in Texas, not knowing what he has just given us.

Find f(1) to five decimal places, and please, do not compromise our national security with this knowledge! Send it directly to Vice President Gore.

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I need some help approaching this word problem, am so lost.

 

[Deleted member 4993]

[SIZE=+3]The Secret Presidential Function


[/SIZE]I need some help approaching this word problem, am so lost.

President Clinton derives all his mystical power from a secret power function. This function is so secret that no one person knows all its values. Vice President Gore, knows all about the function at x = 1. His running mate, Joe Lieberman, knows all about the function at x = 0.9. In a silent auction, an in-the-closet democrat and classmate Mr. Strickland bought the information about x = 0.8, and so on.
Thus, if Gore could only find f(1), he could win the election and run the whole show!
So we get Bush Jr. to talk. He is angry, because he knows about the function at x = 0 and believes that is enough to make him President -- but it is not enough. He knows that

, and so forth. "Wow," we say, "your dad trusted you with a really big secret!"
"What are you talking about?" Bush Jr. complains. "Yeah, I know a lot about the function, but just at the measly point x = 0! I know nothing about f(1), which is what I need to steal the election from Gore! Erm... not that I would want to, of course. Heh, heh, ahem."
We dismiss Bush Jr., and he goes back to his ranch in Texas, not knowing what he has just given us.
Find f(1) to five decimal places, and please, do not compromise our national security with this knowledge! Send it directly to Vice President Gore.

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[Bob Brown MSEE]

"knows all about"

3 people "knows all about" f(x).
You need f(1).
Bush is the only one that shared what he knows with you.
Ignore Al Gore and everything else.

Problem:
Given

Find
f(1)

Approach:
1: Create a truncated power series (use Taylor polynomial)
2: Evaluate at f(1).

Use error term to determine number of terms required to meet accuracy requirement.