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Laplace domain to time domain

1. Homework Statement

i have a question about laplace transforms. I had to find the maximum of a three exponential equation f(t). What I have done is took the first derivative of f(t) and equated it to zero. Now f'(t) is also a three exponential equation ( like f'(t)= e^at +e^bt +e^ct). So I have taken laplace transform for f'(t) = sf(s)-f(0) and obtained a 3rd digree equation in "s". I have solved the cubic equation for f(s) and found out three values of s. Now I need to find out "t" at which f(t) is max.

How can I convert "s= some constant" to "t" ? Can anybody help me out??



2. Homework Equations



3. The Attempt at a Solution
 

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