What is the difference between the maximum value and the extreme value of the derivative?

1. All extreme values are in line with dy dx=0, that is, y'=0;

2. The maximum value and minimum value may be the maximum value and the minimum value, such as y=sinx, y=cos2x.

3. The maximum value and minimum value are not necessarily the maximum value and the minimum value. For example: y=x -x(-5 x 5).

The maximum value is between x=-1 and x=0, and the minimum value is between x=0 and x=1.

The minimum value is at x=-5 and the minimum value is at y=-120;The maximum value is at x=5 and the ymax=120

4. At the maximum and minimum values, there may be dy dx=0, and may be dy dx≠0; At the maximum and minimum values, one point has dy dx=0

The maximum and minimum values are determined by the function image;

The maximum, the minimum, may be determined by the image of the function or by the interval we have given.

There are too many, if the landlord has specific questions, welcome to discuss them together.

The maximum value is a global concept, while the extreme value is a local concept. Such as:

Knowing the function f(x)=x3+2x2-5, find the extreme value of (1)x when it belongs to (-1,6).

2) The maximum value when x belongs to [-1,6].

The extremum of a derivative is the maximum or minimum of a function.

An extreme value is the maximum or minimum value of a function. If a function is in a neighborhood at a point.

There is a definite value everywhere in it, and the value at that point is the maximum (small), and the value of this function at that point is a maximum (small) value.

If it is larger (smaller) than the value of the function at all other points in the neighborhood, it is a strictly maximum (small). This point is accordingly called an extreme point.

or strict extreme points.

Definition of extremum.

The extreme value is the variational method.

a basic concept. Functional.

The maximum or minimum value obtained within a certain range of the allowable function is called the maximum or minimum value, respectively, and is collectively referred to as the extreme value. The variable function that brings the functional to an extreme value is called an extreme function, and if it is a univariate function, it is often called an extreme curve. Extremum is also known as relative extremum or local extremum.

Extremum is a collective term for "maximum" and "minimum". If the value of a function at a point is greater than or equal to the value of the function at that point near any other point, the value of the function at that point is said to be the "maximum" of the function. If the value of a function at a point is less than or equal to the value of the function at any point near that point, the value of the function at that point is said to be the "minima" of the function.

The extremum of a derivative is the maximum or minimum of a function.

An extreme value is the maximum or minimum value of a function. If a function is in a neighborhood at a point.

There is a definite value everywhere, and the value at that point is the maximum and smallest, and the value of the signal cover at that point is a maximum. If it is a function value that is smaller than the other points in the neighborhood, it is a strictly large and small. This point is accordingly referred to as an extreme point.

or strict extreme points.

Meaning of Derivative:The derivative is calculus.

important foundational concepts in . Derivatives are local properties of functions. The derivative of a function at a point describes the rate of change of the function around that point.

Derivatives and differentiation are two important concepts in differentiation, and the study of various properties of functions and the calculation or approximation of function values are inseparable from derivatives and differentiation, and derivative sock and differentiation are universal and effective tools to solve these problems.

The extreme value of a derivative is the maximum, or minima, of a function. An extreme value is the maximum or minimum value of a function. If a function is in a neighborhood at a point.

There is a definite value everywhere in it, and the value at that point is the maximum (small), and the value of this function at that point is a maximum (small) value. If it is larger (smaller) than the value of the function at all other points in the neighborhood, it is a strictly maximum (small). This point is accordingly referred to as an extreme point.

or strict extreme points.

Meaning of Derivative:The derivative is calculus.

important foundational concepts in . Derivatives are local properties of functions. Be cautious: The derivative of a function at a certain point describes the rate of change of the function at that point.

Derivatives and differentiation are two important concepts in differentiation, and the study of various properties of functions and the calculation or approximation of function values are inseparable from derivatives and differentiation, and derivatives and differentiation are universal and effective tools to solve these problems.

(2) The maximum value of the function.

The function y f(x) is greater than the value of its function at the point x=b f(a) is greater than the value of its function at all other points near the point x=b, f'(b) = 0, and f on the left near the point c = b'(x) 0, right f'(x) 0, then the point b is called the maximum point of the function y f(x), and f(b) is called the maximum value of the function y f(x).

The minimum and maximum points are collectively referred to as extreme points, and the maximum and minimum values are collectively referred to as extreme <>

(2) The maximum value of the function.

The function y f(x) is greater than the value of its function at the point x=b f(a) is greater than the value of its function at all other points near the point x=b, f'(b) = 0, and f on the left near the point c = b'(x) 0, right f'(x) 0, then the point b is called the maximum point of the function y f(x), and f(b) is called the maximum value of the function y f(x).

The minimum and maximum points are collectively referred to as extreme points, and the maximum and minimum values are collectively referred to as extreme <>

(2) The maximum value of the function.

The function y f(x) is greater than the value of its function at the point x=b f(a) is greater than the value of its function at all other points near the point x=b, f'(b) = 0, and f on the left near the point c = b'(x) 0, right f'(x) 0, then the point b is called the maximum point of the function y f(x), and f(b) is called the maximum value of the function y f(x).

The minimum and maximum points are collectively referred to as extreme points, and the maximum and minimum values are collectively referred to as extreme <>

Because the function f(x) = x 3 + ax 2 + bx + 1, f'(x)=3x 2+2ax+b, when f'(x)=0, there are 3x 2+2ax+b=0

then =4a 2-12b

So, when <0, i.e., a 2<3b, and the equation 3x +2ax + b=0 has no real root, then the function f(x) has no extremum;

When =0, i.e., a 2 = 3b, the equation 3x 2 + 2ax + b = 0 has a root, and the function f(x) has an extremum;

When >0, i.e., a 2>3b, the equation has two roots, then the function f(x) has two extremums.

f(x) =x^3+ax^2+bx+1

f'(x) =3x^2+2ax+b

1) There are no extremums.

2a)^2 - 4(3)(b) <0

4a^2-12b<0

a^2-3b<0

2) 1 extremum.

a^2-3b=0

3) 2 extremes.

a^2-3b > 0

f'(x)=3x 2+2ax+b, when >0, there are two extremums, and when 0, there may be no extremum.

First find the derivative, then let the derivative equal to 0 to get the possible extreme point, then judge the monotonicity by judging the positive and negative of the derivative, and finally get the extreme value, and then calculate the endpoint value, compare the size, the maximum is the maximum value, and the minimum is the minimum value.

Not all functions have derivatives, and a function does not necessarily have derivatives at all points. If a function exists at a certain point in derivative, it is said to be derivable at that point, otherwise it is called underivable. However, the derivable function must be continuous; Discontinuous functions must not be derivative.

For the derivative function f(x), x f'(x) is also a function called a derivative of f(x). The process of finding the derivative of a known function at a point or its derivative is called derivative.

Sophomore Mathematics: Using derivatives to study the extreme and maximum values of functions.