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Increasing/decreasing intervals & extremum points challenge

Define the function ff by the equation
f(x)=ex(x2)\qquad f(x)=e^x(x-2)\,.
The function has one critical number (critical point) at x=cx=c.
What is the numerical value of the critical number cc\,?
c= c=~
Is  f(c) \displaystyle~f(c)~ a local minimum, a local maximum, or neither?
f(c)f(c) is