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Dear student,
I will give only hint not the full solution:
A function f(x) is said to have a local maximum at x = a, if $ is a neighbourhood I of 'a', such that
f(a) f(x) for all x I
The number f(a) is called the local maximum of f(x). The point a is called the point of maxima.
Note that when 'a' is the point of local maxima, f(x) is increasing for all values of x < a and f (x) is decreasing for all values of x > a in the given interval.
At x = a, the function ceases to increase.
A function f(x) is said to have a local minimum at x = a, if $ is a neighbourhood I of 'a', such that
Here, f(a) is called the local minimum of f(x). The point a is called the point of minima.
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