Instruction

Find the largest , which on the segment has a finite number critical points. To do this, calculate meaning at all points, as well as at the ends of the segment. From the received, choose the largest. Finding the largest value method expressions to solve various applied tasks.

To do this, perform the following steps: translate the problem into the language of the function, select the parameter x, and express the desired value in terms of it as a function f(x). Using analysis tools, find the largest and smallest values ​​of the function on a certain interval.

Count the number necessary action and think about the order in which they should be done. If it bothers you this question, note that the actions enclosed in brackets are performed first, then division and multiplication; and the subtraction is done last. To make it easier to remember the algorithm of the actions performed, in the expression above each action operator sign (+, -, *, :), with a thin pencil, write down the numbers corresponding to the execution of the actions.

Proceed with the first step, adhering to the established order. Count mentally if the actions are easy to perform verbally. If calculations are required (in a column), write them under the expression, indicating serial number actions.

Clearly track the sequence of actions performed, evaluate what needs to be subtracted from what, what to divide into what, etc. Very often, the answer in the expression turns out to be incorrect due to errors made at this stage.

To find the set of values ​​of a function, you first need to know the set of values ​​of the argument, and then, using the properties of inequalities, find the corresponding maximum and minimum values ​​of the function. This is the decision of many practical tasks.

Instruction

Find the largest value of a function that has a finite number of critical points on a segment. To do this, calculate meaning at all points, as well as at the ends of the segment. From the received numbers, choose the largest. Finding the largest value method expressions used to solve various applied problems.

To do this, perform the following steps: translate the problem into the language of the function, select the parameter x, and express the desired value through it as a function of f(x). Using analysis tools, find the largest and smallest values ​​of the function on a certain interval.

Take advantage the following examples to find the value of the function. Find function values ​​y=5-root of (4 – x2). Following the definition square root, we get 4 - x2 > 0. Decide quadratic inequality, as a result you get that -2

Square each of the inequalities, then multiply all three parts by -1, add 4 to them. Then introduce an auxiliary variable and make the assumption that t = 4 - x2, where 0 is the value of the function at the ends of the interval.

Make the reverse change of variables, as a result you will get the following inequality: 0 value, respectively, 5.

Use the Apply Properties Method continuous function to determine the largest meaning expressions. AT this case use numerical values, which are accepted by the expression on given segment. Among them there is always the smallest meaning m and the largest meaning M. Between these numbers lies a set of function values.

To find the set of values ​​of a function, you first need to know the set of values ​​of the argument, and then, using the properties of inequalities, find the corresponding maximum and minimum values ​​of the function. This leads to the solution of many practical problems.

Instruction

• Find the largest value of a function that has a finite number of critical points on a segment. To do this, calculate its value at all points, as well as at the ends of the segment. From the received numbers, choose the largest. Finding the largest value method expressions used to solve various applied problems.
• To do this, perform the following steps: translate the problem into the language of the function, select the parameter x, and express the desired value through it as a function of f(x). Using analysis tools, find the largest and smallest values ​​of the function on a certain interval.
• Use the following examples to find the value of a function. Find function values ​​y=5-root of (4 – x2). Following the definition of the square root, we get 4 - x2 > 0. Solve the quadratic inequality, as a result you get that -2
• Square each of the inequalities, then multiply all three parts by -1, add 4 to them. Then introduce an auxiliary variable and assume that t = 4 - x2, where 0
• Make a reverse change of variables, as a result you will get the following inequality: 0
• Use the method of applying the properties of a continuous function to determine highest value expressions. In this case, use the numeric values ​​that are accepted by the expression on a given segment. Among them there is always smallest value m and the largest value M. Between these numbers lies the set of values ​​of the function.