# Function. The order of finding the largest and smallest value of a continuous function on an open or

- Algebra Calculators
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- Function. Types, properties of functions.
- Algebra 6,7,8,9,10,11 class, EGE, GIA
- Function. Necessary criteria for extremum.

The sequence of calculations to determine __ the smallest and largest function values __ in the open or

**infinite interval**consists of the following steps.

Set whether the interval *X is a* **subset** __ function definition areas __

**.**

Select the **set of points** where the first one does not exist. __ derivative __ and which are located on the interval

*X*(traditionally these points are found in

__with the argument under the__

**functions****sign of the modulus**and

**power functions**with a fractional rational index). When these points are not, then proceed to the next stage.

Set the **set of stationary points** located in the interval *X.* For this purpose, the **derivative of the function is** equated to zero, we find __ the roots __ the resulting

**equation**and take only suitable. When there are no stationary points or none of them is in the interval, then proceed to the next stage.

We perform calculations of the **function** values at stationary points and points at which the first derivative of the function does not exist (if there are such points).

As you can see, the sequence of performing actions up to this point was no different from __ finding the largest and smallest value of the function on the segment __ . Further, the course of calculations is determined by the interval

*X.*

When interval *X is* characterized as:

*(a; b)* , calculate **one-sided limits** ;

*(a; b]* , set the value of the **function** at *x = b* and one-sided **limit** ;

*[a; b)* , set the value of the **function** at *x = a* and one-sided limit ;

(- ∞; + ∞), we make calculations __ limits __ by + ∞ and -∞ ;

[ *a* *;* *+ ∞)* , perform calculations of the value of the function at the point *x = a* and the limit at + ∞ ;

( *a* *; + ∞)* , we **calculate the one-sided limit** and limit by + ∞ ;

(-∞; *b* ] set the value of the function at *x = b* and the limit at -∞ ;

(-∞; *b* ) find the one-sided limit and the **limit** is -∞ ;

Having obtained the values of the **function** and limits, we carry out a sequential analysis. Many answers may be received. So, when the one-sided limit equals **minus infinity** (plus infinity), then o __ maximum (minimum) value of the function __ nothing can be said for the selected interval.

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Solutions, tips and a textbook of linear algebra online (all calculators for algebra). __ Algebra Calculators __

## Math Calculators

Mathematical calculators: roots, fractions, degrees, equations, figures, number systems and other calculators. __ Math Calculators __

## Function. Types, properties of functions.

Linear, power, logarithmic, exponential function; monotony, definition of functions __ Function. Types, properties of functions. __

## Algebra 6,7,8,9,10,11 class, EGE, GIA

Basic information on the course of algebra for education and training in the exams, GDE, EGE, OGE, GIA __ Algebra 6,7,8,9,10,11 class, EGE, GIA __

## Function. Necessary criteria for extremum.

The points at which the necessary extremum criteria (conditions) are realized for the case of a continuous function are designated as critical points of the function. __ Function. Necessary criteria for extremum. __