Calculating Recursive Derivatives at Point x=0

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Homework Help Overview

The discussion revolves around calculating the recursive derivatives of a function at the point x=0, specifically focusing on the expression f(f(f(x))) given certain initial conditions for the function and its derivative.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the implications of the initial conditions f(0) = 0 and f'(0) = 1, questioning the relevance of derivatives in the context of recursive function evaluation.

Discussion Status

The conversation has evolved to clarify the original question about calculating the derivative of f(f(f(0))). Some participants have provided insights into the differentiation process, leading to a potential simplification, although no consensus has been reached on the final outcome.

Contextual Notes

There appears to be some confusion regarding the initial problem statement and the role of derivatives in the calculation, with participants questioning the setup and assumptions involved.

Monsu
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hi, could smne pls give me an idea of how to deal with this problem?

Suppose that f(0) = 0 and that f'(0) =1 , calculate f(f(f(x))) at point x=0
thanks a lot, any hint at all would b helpful, as i completely clueless.
 
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if f(0) = 0 then f(f(0)) = f(0) = 0.. it's recursive. I am not sure why you would need f'(x) to solve nothing to do with derivatives. Are you sure you typed the question correctly?
 
here it is again:
f(0) = 0 and f'(0) = 1 calculate the derivative of f(f(f(x))) at point x=0

that's the exact question.
thanks for the help on the second question
 
Last edited:
Oh I see calculate the DERIVATIVE of f(f(f(0)))

First let's set g(x) = f(f(x))
g'(x) is therefore f'(f(x))*f'(x)

Derivative f(g(x)) after substitution is f'(g(x))*g'(x)

= f'(f(f(0)))*f'(f(0))*f'(0)

What a mouthful. If I were to venture a wild crazy guess I'd say that simplifies to 1.
 
oh great! i just worked it out, it did come to 1. thanks a lot.
can u give a further hint on the other question, I'm still a bit confused there.
thanks again, marvellous!
 

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