Minimum value of n for non-zero 4th derivative in Euler-Bernoulli beam equation

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SUMMARY

The discussion focuses on determining the minimum value of n in the term ax^n for which the fourth derivative is non-zero in the context of the Euler-Bernoulli beam equation. Participants suggest using Wolfram Alpha to compute derivatives, emphasizing that if n is less than 4, the fourth derivative will be zero. Therefore, the minimum value of n must be 4 to ensure a non-zero fourth derivative, which is critical for accurately modeling beam behavior in structural engineering.

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  • Understanding of calculus, specifically derivatives
  • Familiarity with the Euler-Bernoulli beam theory
  • Basic knowledge of polynomial functions
  • Experience using computational tools like Wolfram Alpha
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Structural engineers, mathematicians, and students studying mechanics of materials who need to understand the significance of higher-order derivatives in beam theory.

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Prove that this equation satifies the Euler-bernoulli beam equation which is given by

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Cany anyone help me with this. Can wolfram alpha do it? It has so many values and I'm not comfartble with doing 4th derivitives
 
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You don't have to do all the derivatives. If you have some term like ax^n, where a is a constant, what is the min value of n so that the 4-th derivative is not zero? What is its value in the min case?
 

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