How to judge the number of real roots of some transcendental equations by derivative? For some transcendental equations, it is impossible to find the root directly Is there any way to judge the number of roots?

How to judge the number of real roots of some transcendental equations by derivative? For some transcendental equations, it is impossible to find the root directly Is there any way to judge the number of roots?

The number of roots is generally determined by image method. The general direction of image can be obtained by derivative method, and then the number of solutions can be determined
In addition, although the image method is vivid, the solution error is too large. The commonly used approximate solutions include Newton tangent method, power series method, etc. now we can also compile a program to solve it by computer, or use ready-made software to solve it. For example, excel installed in most computers can also be used to solve transcendental equations

How to discuss the number of real roots of cubic equation
This paper discusses the number of real roots of the equation AX ^ 3 + BX ^ 2 + CX + D = 0 (a > 0)

Let f (x) = ax ^ 3 + BX ^ 2 + CX + D (a > 0)
If there is no extremum, then f (x) increases in R, and the original equation has only one real root;
If there is an extreme value (it must be a max min), then when the maximum value of F (x) is less than 0 or the minimum value of F (x) is greater than 0, the original equation has and only has one real root; when the maximum value of F (x) is equal to 0 or the minimum value of F (x) is equal to 0, the original equation has and only has two different real roots; when the maximum value of F (x) is greater than 0 and the minimum value of F (x) is less than 0, the original equation has and only has three real roots
Note: a

Using derivative to judge the root of transcendental equation
If the equation (x + 1) 2-in (x + 1) 2 = x2 + X + a about X has exactly two different real roots on [0,2], find the value range of real number a
The detailed process can be replaced by photos

After the derivation of both sides, we can get a quadratic equation of one variable, and then we can solve it from the image or by using the Veda theorem. Let's calculate it by ourselves, it's not difficult

Determination of derivative root of equation
If a and B are two different real roots of the equation f (x) = 0, and f (x) is continuous on [a, b] and differentiable in (a, b), then the equation f '(x) = 0 is in (a, b) (). A has only one root, B has at least one root, C has no root, D. all the above conclusions are wrong

B has at least one root

Who can tell me the root piercing method of derivative function

It is true that the point with derivative 0 is not necessarily an extreme point, and the derivative at the extreme point must be 0, because it is possible that the derivative is an expression with multiple roots. At this time, derivative 0 does not mean that it is an extreme point, and the values on both sides of the extreme point are less than it. Moreover, the monotonicity of the function at the extreme point must be opposite, so the derivative of the function at the extreme point must be 0 The monotonicity can be determined by the method of penetrating roots, but we must pay attention to the phenomenon of multiple roots

What is the relationship between the zero point of function and the extreme point of derivative?

The zero point of derivative function is the extremum of function

How to find the number of zeros of a function?

Let function = 0, find all solutions, and the number of solutions is the number of 0 points. For unconventional functions, we take the idea of combining number and shape to see the intersection of functions on both sides of the equation
Hope to inspire you

How to judge the number of zeros of a function
How to solve this problem without drawing? If it is a complex function, how to draw a picture

For the problem of finding the number of zeros of a function,
If the function in the title is a common function, such as primary function, quadratic function, exponential function and so on, it is generally to draw a picture
If the function in the question is more complex, you should first see if you can make it equal to two simple functions, draw two functions, and then look at the number of intersections
If the function of the problem becomes the equal form of two simple functions, if it is derived mathematically, we can use the property of derivative to consider the monotonicity of the function first and then find it

How to judge how many zeros a function has? And how to judge whether a function has zeros?

The first step is to find the derivative of the function and judge its monotonicity. The second step is to determine whether the function has zeros according to the monotone interval. Of course, you don't give the specific function, so you can only provide solutions,

How to judge the number of zeros of a function
The number of zeros of the function y = x to the third power - x to the square - x + 3 (please attach the analytic process)

y=x^3-x^2-x+3
y'=3x^2-2x-1=(3x+1)(x-1)
y"=6x-2=2(3x-1)
f(-1/3)=-1/27-1/9-1/3+3>0
f(1)=2>0
Decrease in (- 1 / 3,1) interval, so there is no zero in this interval
In the interval of x > 1, there is no zero
There is only one zero in X