QuestionQuestion

Order the following super-funky functions f(n) from fastest to slowest (if used to evaluate run time):

n
n!
log(n!)
eⁿ
log(logn)
logn
nlogn
n*2ⁿ
1/n

Pick any two functions, f( n ) and g( n ), that are adjacent in your ordering above. Find the first n0 such that f( n ) < g( n ) for all n larger than n0.

How can the derivative be used to find out the asymptotic relationship between two functions?
For example, the derivative of n is 1 and the derivative of n² is 2n - what does this mean?

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