Finding the maximum value of an equation, how to find the minimum or maximum value of an equation?

36x/(10+x)^2

36x (100+20x+x 2) (denominator)36 (20+x+100 x) (the numerator denominator is divided by x), since x>0 , so x+100 x>=2 100=20 is obtained from the mean inequality, and if and only if x=100 x i.e. x=10 x takes the minimum value of 20, so when x=10, the original formula has a maximum value of 36 (20+20)=9 10.

Typing is not easy, such as satisfaction, hope.

This is usually done here:

n as the horizontal axis and m as the vertical axis, and when you draw it, you will see that the area to the right of the line is 1000, which is not the area we are talking about. And we ask n>0, m>0, we draw a straight line (i.e., the coordinate axis) of n=0, m=0, and the triangle where the three lines intersect is the range we want to discuss, and then slowly find it. Sorry, this method is not the same, this is called linear programming).

I observe, then 125*8=1000, so m=n=125, which is a coincidence. = =

First, look at the quadratic coefficient.

Yes is exactly negative, if it is positive, it means that the curve opening is up, then find x=-b (2a), and then find the y value is the minimum value of the equation. If the quadratic coefficient is negative, the corresponding y-value is the maximum value of the equation.

One-element quadratic equation solution.

1. Kaiping method.

The Kaiping method is a more commonly used solution to a quadratic equation, and the main form is similar to x?=n(n≠0), i.e. the equation has an unknown on one side and a non-negative number on the other, so that it can be solved by the open square root.

2. Matching method.

The collocation method is also often used when solving one-dimensional quadratic equations, which mainly uses four steps: shift, coefficient1, formulation, and solution. This is a relatively simple method that students can try when doing the same problem.

3. Formula method.

The general formula for a quadratic equation is a x?bx c=0(a≠0), we can derive what is the root of x based on this, and then study and analyze the b?-4ac is greater than 0, less than 0, and equal to 0, and the real solution of the equation is calculated.

Remind students to pay attention to the need to first solve it into a general formula when using this method, and then determine the values of a, b, and ascending number c.

4. Factorization.

It is mainly to perform related shifting operations on the two equations, and then add and subtract the two equations to find the real root.

When the equation contains alphabetic coefficients, this method should be used to pay attention to the higher coefficients of the coefficients, and then determine the class grandchild of the equation.

The maximum value of the function is calculated as follows:

1) For any x i, there is f(x) m;

This sentence means that the value of the function in the definition domain of the function is less than or equal to a number (m).

2) There is x0 i such that f(x0)=m

This sentence means that in the domain of the definition of the celery number of the source, there should be such a thing as a function equal to x0 of m.

Finding the extreme value of hail is generally done by derivative, and its first derivative is equal to 0.

The maximum value is the largest value in the known data, and in mathematics, the maximum value of the function is often found, and the general solution methods include the commutation method, the discriminant method, the function monotonicity method, the number combination method and the derivation method.

It can be seen that the equation is proportional to z with respect to x and y.

So the larger the x and y, the bigger the z.

Then, when x=1599 and y=9999, z is the largest, and the integer is taken.

z=750+

RMS value of sinusoidal alternating current = maximum value 2 = maximum value; Or maximum = 2 RMS = RMS.

The RMS value of the current is specified according to the thermal effect of the current: let the alternating current and the constant current pass through a resistor of the same resistance, and if the thermal effect of the two is equal (i.e., the same heat is generated in the same time), then this equivalent DC voltage, the value of the current is called the AC voltage, the RMS value of the current).

In order to measure the work done by alternating current, a RMS value is introduced, which is based on the thermal effect of the electric current. That is, the value of the direct current is the effective value of the alternating current when the direct current passes through the resistance of the same resistance value and the heat generated in the same time.

1. Find the maximum value by the commutation method.

The maximum value of the commutation method mainly includes triangular commutation and algebraic commutation, and special attention should be paid to the range of intermediate variables.

2. Discriminant to find the maximum value.

It is mainly suitable for functions that can be reduced to quadratic equations about independent variables.

3. Combination of numbers and shapes.

It is mainly suitable for functions whose geometry is more clear, and the geometric model is used to find the maximum value of the function.

4. Function monotonicity.

First, the monotonicity of the function in a given interval is determined, and then the maximum value of the function is found according to the monotonicity.