Instruction

1

Follow finding the maximum value of the function, which in the interval has a finite number of critical points. To do this, calculate its

**value**at all points and at the ends of the segment. From the resulting numbers, choose the highest. The method of finding the greatest value**of the expression**is used to solve various application tasks.2

To do this, run the following steps: translate the task into the language of the function, select x, and through him to Express the required rate as a function of f(x). Using Analytics, find the largest and smallest values of the function at a certain interval.

3

Use the following examples to find the value of the function. Find the values of the function y=5-square root (4 – x2). Using the definition of the square root, we get 4 - x2 > 0. Solve the quadratic inequality, we get that -2 < x < 2. Divide the resulting interval into two, you get two inequalities -2 < x < 0 and 0 < x < 2.

4

Erect in the square each of the inequalities, then multiply all three parts by -1, add to them 4. Then enter the auxiliary variable and make the assumption that t = 4 - x2, where 0 < t < 4. A function of y, is the square root of the variable t on the interval is increasing and continuous. Therefore, the greatest

**value**of the function happens at the end of the period.5

Perform the inverse change of variables, as a result, you will get the following inequalities: 0 < root of (4 – x2) < 2. Add to all portions 5, before multiplying by -1, you get 3 < 5 - root of (4 – x2). < 5. Thus, the set of values of the function y = 5 - square root (4 – x2) is the interval [3; 5], and the largest

**value**, respectively, 5.6

Use the method of application properties of continuous functions to determine the highest

**value****of the expression**. In this case, use the numeric values taken by the expression at the specified interval. Among them, there is always a least**value**m and maximum**value**M. Between these numbers is a set of values of the function.