The number of intersections of function f (x) = x ^ 3-6x ^ 2 + 9x-10 and y = - 8 is

The number of intersections of function f (x) = x ^ 3-6x ^ 2 + 9x-10 and y = - 8 is

1. Because the origin is symmetric, let y = f (x) point (x, y), then the point (- x, - y) is on the following function
It satisfies - y = (- 2x + 1) / (- x-3),
After transformation, y = (1-2x) / (x + 3)
2. Any XO belongs to [0,1]
The range of F (XO) is [0,1]
Then the meaning of the title can be transformed into "always exist X1 belongs to [0,1], so that G (x1) belongs to [0,1]"
And because x = (g (x) + 2a-5) / a = (g (x) - 5) / A + 2
X [Max] = - 4 / A + 2 = 1, then a = 4
X [min] = - 5 / A + 2 = 0, then a = 5 / 2
so,a[max]=4
3. E ^ x is an increasing function, so don't consider it
Derivation of the part in brackets
Let g (x) = (1 + x-x ^ 2)
We get: G (x) '= 1-2x
Because it requires an increasing interval,
so g(x)'=1-2x>=0
We get X & lt; = 1 / 2
4. If f (x) '= 3ax ^ 2 + 1 / x = 0, there is a solution
so a≠0
5.f(x)=2f(2-x)-x^2+8x-8 ---- ①
Let t = 2-x
Then f (T) = f (2-x) = 2F (x) - (2-x) ^ 2 + 8 (2-x) - 8
The reduction is f (2-x) = 2F (x) - x ^ 2-4x + 4 ----- ②
Consider f (2-x) and f (x) as two unknowns, and eliminate f (2-x)
So f (x) = x ^ 2
so f(x)'=2x
6. Let f (x) = x ^ 3-6x ^ 2 + 9x
The derivative is f (x) '= 3x ^ 2-12x + 9
Let f (x) '= 3x ^ 2-12x + 9 = 0
We can get x = 1, x = 3
So [negative infinity, 1] & [3, positive infinity] is an increasing function
[1,3] is a decreasing function
You can make a graph
When x = 1, f (x) = 4
When x = 3, f (x) = 0
So f (x) = 10, i.e. there is only one intersection of F (x) and y = 10
A real number root

Given the function f (x) = x ^ 3-6x & # 178; + 9x-3, find the extremum of function f (x)

f'(x)=3x²-12x+9=0
x²-4x+3=0
x=1 x=3
When x = 2, f '(2) = 3 * 4-12 * 2 + 9 = - 3

Given the function f (x) = x & # 179; + ax & # 178; + BX + C, when x = - 1, we get the maximum value 7, when x = 3, we get the minimum value, ask the value of AB and find the minimum value of F (x)

f'(x)=3x^2+2ax+b
From the meaning of the title, we can know
f(-1)=-1+a-b+c=7,f'(-1)=3-2a+b=0,f'(3)=27+6a+b=0
a = -3 ; b = -9 ; c = 2
F (x) minimum f (3) = 27-27-27 + 2 = - 25

Given the function y = ax & # 179; + BX & # 178;, when x = 1, there is a maximum value of 1: (1) find the analytic expression of the function
Given the function y = ax & # 179; + BX & # 178;, when x = 1, there is a maximum value 1: (1) find the analytic expression of the function; (2) find the minimum value of the function

(1)1=a+b①
y'=3ax²+2bx
If x = 1 is substituted, there will be
3a+2b=0②
Solution
a=-2,b=3
y=-2x³+3x²
(2)y'=-6x²+6x
=-6x(x-1)=0
x=0
y''=-12x+6
y''(0)=6>0
There is a minimum y (0) = 0

What is the maximum and minimum value of the function y = a + 48x-x & #179;? The most important thing is to have a process

y'=48-3x²
Let y '> = 0
48-3x²>=0
x²

The maximum value of function y = x|x (x + 3) | + 1 is? And the minimum value is? Solving process

1) First, write the function in the form of segments
f(x)=｛x^3+3x^2+1 (x

The difference between the maximum and minimum of function and the maximum and minimum of function
It is said in the book that the extreme value of a function is different from the maximum and minimum value of a function in a certain interval. What is the difference between them?

The maximum and minimum are considered globally. If there is a maximum, there is only one
If f (x) is continuous at point a, if the left side increases and the right side decreases, then f (a) is called the maximum, otherwise it is called the minimum
Therefore, a function may have several maxima or minima
The maximum of a function may or may not be the maximum. Similarly, the minimum of a function may or may not be the minimum

Is there any difference between maximum and maximum?

In fact, the extremum is for the differentiable function. If the value of the function at x0 is larger (or smaller) than that near it, then the value of the function at x0 is a maximum (or minimum) value of the function. In other words, the differentiable function must make f '(x) = 0 at the extremum
The maximum and minimum are for the whole function, which is equivalent to the boundary of the function in the domain

What's the difference between the minimum and the minimum, the maximum and the maximum in a certain interval of a function?

The difference is that the maximum value and the minimum value are the maximum value and the minimum value of the range in the function domain
The maximum and minimum values are the maximum and minimum values of a subset in the domain of the function
In other words, the domain of definition can be divided into multiple intervals to investigate the range of its range, that is, the maximum and minimum

The maximum of a function can be larger than the maximum, right

Wrong, we can only say that the maximum value of the function is greater than or equal to its maximum value