How to find the greatest least value of a function

Outstanding German mathematician Carl Weierstrass proved that for each continuous function on the interval, there are its maximum and minimum value on this interval. The problem of determining the largest and smallest values of the function has a wide application value in Economics, mathematics, physics and other Sciences.

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How to find the greatest least value of a function

Let the function f(x) is continuous and defined on a given interval [a; b] and has on it some (finite) number of critical points. First, find the derivative function f'(x) h.

2

Equate the derivative of the function to zero to determine the critical points of the function. Do not forget to specify the point at which the derivative does not exist, they are also critical.

3

Of the many found the critical points we select those which belong to the segment [a; b]. The computed values of the function f(x) at these points and at the ends of the segment.

4

From the set of found values of the function to select the maximum and minimum values. This is the desired maximum and minimum values of the function.

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See also

How to find the point of maximum and minimum

How to determine the intervals of monotonicity

How to find maximum value of function

How to find the value of the function

How to find the extremum of function of two variables

How to determine the critical point

How to find the intervals of monotonicity and extremum