To find the set of values of a function, you first need to find out the set of values of the argument, and then, using the properties of inequalities, find the corresponding largest and smallest values of the function. This comes down to solving many practical problems.
Instructions
Find the largest value of a function that has a finite number of critical points on a segment. To do this, calculate it meaning at all points, as well as at the ends of the segment. From the resulting numbers, choose the largest. Method for finding the largest value expressions used to solve various applied problems.
To do this, perform the following steps: translate the problem into function language, select the parameter x, and use it to express the desired value as a function 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 the values of the function y=5-root of (4 – x2). Following the definition of a square root, we get 4 - x2 > 0. Solve the quadratic inequality, the result is -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 the value of the function is 0 at the ends of the interval.
Make a reverse change of variables, as a result you will get the following inequality: 0 value, respectively, 5.
Use the method of applying the properties of a continuous function to determine the largest meaning expressions. In this case, use the numeric values that are accepted by the expression on a given interval. Among them there is always the smallest meaning m and greatest meaning M. Between these numbers lies the set of function values.
To find the set of values of a function, you first need to find out the set of values of the argument, and then, using the properties of inequalities, find the corresponding largest and smallest values of the function. This comes down to solving many practical problems.
Instructions
- 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 resulting numbers, choose the largest. Method for finding the largest value expressions used to solve various applied problems.
- To do this, perform the following steps: translate the problem into function language, select the parameter x, and use it to express the desired value as a function 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 the values of the function y=5-root of (4 – x2). Following the definition of a square root, we get 4 - x2 > 0. Solve the quadratic inequality, the result is -2
- Square each of the inequalities, then multiply all three sides by –1, add 4 to them. Then introduce an auxiliary variable and make the assumption that t = 4 - x2, where 0
- Perform the reverse change of variables, as a result you get the following inequality: 0
- Use the method of applying the properties of a continuous function to determine the largest value expressions. In this case, use the numeric values that are accepted by the expression on a given interval. Among them there is always the smallest value m and the largest value M. Between these numbers lies the set of function values.
Instructions
Find the largest that has a finite number of critical points on the segment. To do this, calculate it meaning at all points, as well as at the ends of the segment. From those received, select the largest. Method for finding the largest value expressions for solving various applied problems.
To do this, perform the following steps: translate the problem into function language, select the parameter x, and use it to express the desired value as a function f(x). Using analysis tools, find the largest and smallest values of the function on a certain interval.
Count the number of actions required and think about the order in which they should be performed. If this question is difficult for you, please note that the operations enclosed in parentheses are performed first, then division and multiplication; and subtraction are 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, following the established order. Count in your head if the actions are easy to perform verbally. If calculations are required (in a column), write them down under the expression, indicating the serial number of the action.
Clearly track the sequence of actions performed, evaluate what needs to be subtracted from what, divided into what, etc. Very often the answer in the expression is incorrect due to mistakes made at this stage.
