Concept of local maximum and local minimum:
Local maximum:
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A function f(x) is having local maximum at x=a if the value of f(a) is greater than all the values of f(x) in a small neighbourhood of x=a.
Mathematically, f (a) > f (a - h) and f (a) > f (a + h) here h > 0, then a is called as point of local maximum.
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Local minimum:
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A function f(x) is said having local minimum at x = a, if the value of function at x = a is less than value of the function at the neighboring points of x = a. Mathematically, f (a) < f (a - h) and f (a) < f (a + h) where h > 0, then a is called as point of local minimum.
A point of the local maximum or a local minimum is called as point of local extremum.
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Fig. Local Minima
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