Finding the maximum of a function

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Why does f attain its local maximum at r' in (p,q). Is it because we have f(x)<= f(r') for all x in (p,p+delta)?
 
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ratio said:
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Why does f attain its local maximum at r' in (p,q). Is it because we have f(x)<= f(r') for all x in (p,p+delta)?
We have equality, but, yes.
 
Thanks for you answer^^
 

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