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reuse values maximize


Sorry, very simple question, but I really can't work it out...

I want to use the output of a maximation for further calculations.
something like:

z[y_]=-y^2+y
a=Maximize[z,{y}]
b=Extract[a,1]

Now mathematica returns {y -> -0.5}. 

I want to assign the value of -0.5 to a new variable. So far I haven't
worked out how to do this (besides copy and paste!).

Thanks for any comment.


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