What is the difference between finding the local maxima/minima and absolute maxima/minima of a differential equation?

Asked by Susan fletcher | 18th Feb, 2014, 11:56: AM

Expert Answer:

The maximum and minimum of a function, are the largest and smallest value that the function takes at a point either within a given neighborhood or on the function domain.
 
A function f has a local minimum at x=a if f open parentheses x close parentheses greater or equal than f open parentheses a close parentheses near r
Similarly, a function f has a local maximum at x=a if f open parentheses x close parentheses less or equal than f open parentheses a close parentheses near a.
A function f has a global minimum at x=a if f open parentheses x close parentheses greater or equal than f open parentheses a close parentheses all over the domain.
Similarly, a function f has a global maximum at x=a if f open parentheses x close parentheses less or equal than f open parentheses a close parentheses all over the domain.
Let us observe the following figure.
 

Answered by  | 18th Feb, 2014, 12:53: PM

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