MAXIMA AND MINIMA 

Analysis  
A function y=f(x) reaches a local MAXIMUM at a point x_{o} when f(x)£f(x_{o}) in the neighbourhood of x_{o }
Similarly we can say that it reaches a local MINIMUM at a point x_{o} when f(x)³f(x_{o}) in the neighbourhood of x_{o }
Let's see what happens when we are working with derived functions.
1. LOCAL MAXIMA AND MINIMA 

A function y=f(x) reaches a local MAXIMUM at x_{o} when f(x)£f(x_{o}) in the neighbourhood of x_{o }
Therefore: 

Similarly y=f(x) reaches a Local MINIMUM at x_{o} when f(x)³f(x_{o}) in the neighbourhood of x_{o }




Now look carefully at the curves of the function y=f(x),its derivative y=f'(x) and the second derivative y=f''(x) in the window.

María José García Cebrian  
Spanish Ministry of Education. Year 2001  
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