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## Homework Statement

Which of the following satisfy (f^k)(x) = 0 for all k >= 6?

a) f(x) = 7x^4 + 4 + x^-1

b) f(x) = sqrt(x)

c) f(x) = x^(9/5)

d) f(x) = x^3 - 2

e) f(x) = 1 - x^6

f) f(x) = 2x^2 + 3x^5

## Homework Equations

None, but given as a problem in a chapter where the topic is higher order derivatives.

## The Attempt at a Solution

I think the answer is e) but it's true for all k not just k>=6 and I don't know how finding the answer relates to higher order derivatives or how I'd use higher order derivatives to find the solution

k >= 6, for x = 1 & -1

(1-1)^k = 0

0^k = 0, lol

Edit: Hmmm maybe I'm reading the problem wrong? Is it asking which function is always = 0 for all x, and all k >= 6?

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