TAILIEUCHUNG - A study on maxima and minima for single real valued function

By the maximum values of a function f (x) in calculus, we do not necessarily mean the absolutely greatest value attainable by the function. A function f (x) is said to be maximum for a value c of x, provided f (c) is greater than every other value assumed by f (x) in the immediate neighbourhood of x = c. Similarly a minimum value of f (x) is defined to be the value which is less than other values in the immediate neighbourhood. | A STUDY ON MAXIMA AND MINIMA FOR SINGLE REAL VALUED FUNCTION Jagat Krishna Pokhrel ABSTRACT By the maximum values of a function f x in calculus we do not necessarily mean the absolutely greatest value attainable by the function. A function f x is said to be maximum for a value c of x providedf c is greater than every other value assumed by f x in the immediate neighbourhood of x c. Similarly a minimum value of f x is defined to be the value which is less than other values in the immediate neighbourhood. Key words function derivatives turning value critical values logical thinking substantial. INTRODUCTION AND MOTIVATION i Maximum value of a function A function f x is said to have a maximum value for x c provided we can get a positive quantity s such that for all values of x in the interval c-S x c s x c f c f x . if f c h -f c 0 for h sufficiently small. c-s c c s ii Minimum value of a function The function f x has a minimum value for x c provided we can get an interval c - S x c S within which f c f x x c . . if f c h -f c 0 for sufficiently small. The maximum and minimum values of a function are also known as relatively greatest and least values of the function in that these are the greatest and the least values of the function relatively to some neighbourhoods of the points in question. The extreme value is used both for a maximum as well as for a minimum value. And while ascertaining whether a value f c is an extreme value of f or not we compare f c with the values of f for values of x in any neighbourhood of c. So that the values of the function outside the neighbourhood do not come into question. Thus a maximum minimum values of a function may not be the greatest least of all the values of the function in a finite interval. In fact a function can have Mr. Pokhrel is Associate Professor in Mathematics Education Sanothimi Campus Sanothimi and currently affiliated with QAA at . 46 A STUDY ON MAXIMA AND MINIMA FOR SINGLE REAL. several maximum and minimum

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• Logical thinking
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• Single real valued function
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