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\noindent {\bf Problem statement} a) Suppose you know that
$f'(x)=(x-1) (x-2)^2 (x-3)^3 (x-4)^4 (x-5)^5$. What are the critical
points of $f$? Which of them are local extrema, and what kind of
local extrema are they?  

\medskip 

\noindent b) Suppose you know that $\displaystyle {g'(x) = x
(x-1)^{2/3} (x-2)^{3/5} (x-3)^{4/7}}$. What are the critical points
of $g$? Which of them are local extrema, and what kind of local
extrema are they?  

\medskip 

\noindent {\bf Note} You are {\it not}\/ asked to compute $f$ and $g$
explicitly.




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