Solve a calculus problem?

Questions
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1

Consider the following code:

$Assumptions = 
     Element[f, Reals] && Element[\[Beta], Reals] && 
      Element[\[Alpha], Reals] && Element[n, Reals] && 
      Element[\[Epsilon], Reals] &&
       \[Alpha] > 0 && \[Beta] > 0 && \[Mu] > 0 && \[Epsilon] > 0 && 
      f > 0 && n > 0

f := 1 - Exp[-\[Beta] (1 - Exp[-\[Alpha]\[Epsilon]])^n]

DSolve[f''[\[Epsilon]] == 0, f[\[Epsilon]], \[Epsilon]]

I get the following error message :

DSolve::ivar: 1-E^(-(1-Power[<<2>>])^n \[Beta]) is not a valid variable.

What is my mistake? What is the correct method?

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2

You gave f a value so it cannot be a dependent variable (the message pretty much states this). Maybe try Clear[f] before running the DSolve.

3

Thanks. I am a newcomer to mathematica.

Yes, your solution did not lead to the old error. But I still do not understand many things. You say that I gave f a value. I was just trying to define my function. Why did Clear not erase the definition?

I will try again with a function where I know the answer. This will hopefully help me to learn what I should do.

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I should get x0 as the solution for f’'[x]==0. The slope at this point should be U/(4*C). How do I get this with mathematica. How should I handle C1 and C[2]? I don’t understand what they mean.