What is the geometric meaning of the maximum value of a function

What is the geometric significance of the maximum value of a function? What is the value of the resellingism that is shirking?

There are three properties of the maximum-value function. They are as follows:

Property 1: Let the function y=f (x) be a continuous derivative function that defines the domain as the interval (a,b), and if x0 (a,b) is the maximum (small) point of the function y=f (x), then f(x)=0

Property 2: Let the function y=f (x) be a continuous derivative function that defines the domain as the interval (a,b), if x0 (a,b) is the maximum (small) point of the function y=f (x), and the function y=f (x) has only one extreme point in the interval (a,b), then x0 is the maximum (small) point of the function y= f (x).

Property 3: Let the function y=f (x) be a convex (concave) function on the interval (a,b) defined domain, and if x0 (a,b) satisfies f(x0)=0, then x0 is the maximum (small) value point of the function y=f (x) and is also the maximum (small) value point.

In general, let the function y=f (x) be defined in the domain i, if there is a real number m satisfying the lead resistance:

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

2) The presence of x0 i makes it.

f （x0）=m.Well, weigh.

m is the maximum value of the function.

By definition, it is not difficult for us to know: if the function.

y=f (x) is defined in the domain i, and for any x i, exists.

x0 i, such that.

f (x) f (x0), then the function.

y=f (x) at x0;

Anti-acre slow, function.

y=f (x), x i, and the maximum value at x0 is obtained.

f (x) f (x0) is constant for any x i.

In general, the maximum value of a function is divided into the minimum value of the function and the maximum value of the function. In simple terms, the minimum value is the minimum value of the function value in the defined domain, and the maximum value is the maximum value of the function value in the defined domain. The geometric significance of the maximum (small) value of the function - the ordinate of the highest (low) point of the function image is the maximum (small) value of the function.

Brief introduction. In general, the maximum value of a function is divided into the minimum value of the function and the maximum value of the function.

Collapse minimum.

Let the domain of the function y=f(x) be i, if there is a real number m satisfies: For any real number x i, there is f(x) m, and x0 i exists. Let f (x0) = m, then we call the real number m

is the minimum value of the function mill bend y=f(x).

Collapse maximum.

Let the domain of the function y=f(x) be i, if there is a real number m satisfies: For any real number x i, there is f(x) m, and x0 i exists. Let f (x0) = m, then we call the real number m

is the maximum value of the function y=f(x).

Collapse this segment once function.

The primary function (linear

function), also known as a linear function, can be represented by a straight line in the x,y coordinate axis, when the value of one variable in a function is determined, it is foolish that the value of another variable can be determined by a one-dimensional equation.

Therefore, the no-nonsense theory is a proportional function, i.e., y=ax(a≠0). Or a normal one-time function, i.e.: y=kx+b

k is any constant that is not 0, b is any real number), as long as x has a range, i.e., z" or x< m (to be meaningful), then the primary function has a maximum or minimum or maximum or minimum value. It is also related to the range of values of a.

Fold when a<0.

When a<0, y decreases with the increase of x, i.e., y is inversely proportional to x. When x is the maximum, y is the smallest, and when x is the smallest, y is the maximum. Example:

2 x 3 then when x=3, y is the smallest, and when x=2, y is the largest.

Fold when a<0.

Question 1: What is the geometric meaning of the function Let the function be defined in and its vicinity, and the amount of change represented by , then the corresponding change in the value of the function is , if there is a limit to the limit, then the function is said to be derivable at the point , and this limit value is called the derivative of the function at the point , denoted as or.

It is called the average rate of change of the function between to , and the derivative of the function at the point is the limit value of the mean rate of change when .

The derivative of the geometrical function at a point is equal to the tangent slope of the corresponding point on the graph of the function, i.e., where is the angle of inclination of the tangent of the crossing and the tangent equation of the crossing point.

Question 2: What does the function z=f(x,y) mean and what is its geometric meaning This is a binary function, z is determined by two independent variables x,y, and if there is a region a on the xoy plane, then a is the domain of the definition of this binary function, then z=f(x,y) is indeed a surface in the Cartesian coordinate system of oxyz space (the plane is a special surface), and any definition of the domain must correspond to a point on the surface, The distance from this point to the xoy plane is the absolute value of z.

Question 3: What is the average value of a function over a certain interval? What is its geometric significance?

5 points The so-called average value of the function in the interval is literally understood as the sum of the function values corresponding to each point in the interval, and the difference is the total number of points. This mean is numerically equal to the definite integral of the function over that interval, divided by the length of the interval (i.e., the upper and lower bound of the definite integral).

As for why it is equal to, you can refer to the definition and derivation process of definite integrals in the examination textbook.

Question 4: Will XP give full play to the performance of the hardware than 98, so that the game runs more smoothly? As a system that has been in service for more than ten years, it has ushered in its own home.

Now, netizens around the world can't help but be in awe of this system that has existed tenaciously at Microsoft for more than a decade. Only by constantly exploring, trying and innovating can we make the system more humane. This is something that XP can't compare to 7 and that.

Definition 1: Let x0 be a point in the domain of f(x) definition, if f(x) f(x) (x) (or f(x) f(x0)) is true for any point x in the field of definition of f(x), then f(x0) is said to be the generalized maximum value (or the smallest value of the most stool code) of f(x).

Definition 2: Let x0 be a point in the f(x) definition domain, if f(x) f(x) (or f(x)>f(x0)) is true for any point x in the definition domain of f(x) that is different from x0, then f(x0) is said to be the true maximum (or minimum) of f(x).

Generally speaking, with an equal sign, such as f(x) f(x0), the point x0 is called the generalized extreme point or the maximum value point of f(x); Without an equal sign, such as f(x)> f(x0), the point x0 is called the true extreme or maximum point of f(x). In general textbooks, the term "broad sense" is often used.

Let the function be defined in and its vicinity, and denote the amount of change of , then the corresponding change in the value of the function is , if there is a limit to , then the function is said to be derivable at the point , and this limit value is called the derivative of the function at the point , denoted as or.

It is called the average rate of change of the function between to , and the derivative of the function at the point is the limit value of the mean rate of change when .

Geometric significance. The derivative of the function at a point is equal to the slope of the tangent of the corresponding point on the graph of the function, i.e., where is the angle of inclination of the tangent of the crossing and the tangent equation of the crossing point.

If the equation f(x,y)=0 can determine the correspondence between y and x, then this equation is called an implicit function.

Implicit functions may not necessarily be written as y=f(x), e.g. x 2+y 2=0. Therefore, according to the function "Let x and y be two variables, and d is a subset of the set of real numbers, if for each value x in d, variable y has a definite value y corresponding to it according to a certain law, the variable y is called a function of variable x, and it is denoted as.

y=f(x).Implicit functions are not necessarily "functions", but "equations".

In fact, in general, functions are equations, but equations are not necessarily functions.

In general, if the variables x and y satisfy an equation f(x,y)=0, under certain conditions, when x takes any value in a certain interval, there is always a unique y value that satisfies the equation, then it is said that the equation f(x,y)=0 determines an implicit function in this interval. As; x+√y-1=0

There is a real number m in the entire defined domain.

There are f(x) m on it

then m is the minimum value of f(x).

If. f(x)≤m

Then m is the maximum value of f(x).

This segment is the most valuable.

In general, the maximum value of a function is divided into the minimum value of the function and the maximum value of the function.

The minimum value of the function.

Let the domain of the function y=f(x) be i, if there is a real number m satisfies: For any real number x i, there is f(x) m, and x0 i exists. Make f

x0)=m, then we call the function m

is the minimum value of the function y=f(x).

The maximum value of the function.

Let the domain of the function y=f(x) be i, if there is a real number m satisfies: For any real number x i, there is f(x) m, and x0 i exists. Make f

x0)=m, then we call the function m

is the maximum value of the function y=f(x).