It is a little difficult: given the ax power of the function f (x) = (x ^ - X-1 / a) e, (a is not equal to 0.1, find the tangent equation of the curve y = f (x) at the point a (0, f (0)). 2, when a = 3, find the minimum value of F (x)

It is a little difficult: given the ax power of the function f (x) = (x ^ - X-1 / a) e, (a is not equal to 0.1, find the tangent equation of the curve y = f (x) at the point a (0, f (0)). 2, when a = 3, find the minimum value of F (x)

Derivation of F (x)
We can get f '(x) = (2x-1) e ^ ax + a (x ^ 2-x-1 / a) e ^ ax
The slope k = f '(0) = - 1-1 = - 2 is obtained by substituting x = 0
And f (0) = - 1 / A
Tangent equation y-f (0) = K (x-0)
y+1/a=-2x
If f '(x) > 0, the monotone increasing interval can be obtained

It is known that f (x) = x square + ax + 3-a. if x belongs to [- 2,2], f (x) is greater than or equal to 0, then the value range of a is obtained

It is shown that the equation x & sup2; + ax + 3-A = 0 both ≤ - 2 or both ≥ 2 case 1: both ≤ - 2x1 + x2 = - a ≤ - 4x1 * x2 = 3-A ≥ 4 discriminant = A & sup2; - 4 * (3-A) ≥ 0 this is the case of no solution case 2: both ≥ 2x1 + x2 = - a ≥ 4x1 * x2 = 3-A ≥ 4 discriminant = A & sup2; - 4 * (3-A) ≥ 0 the solution is a ≤ - 6 so a

Solve the equation x △ 25 + X △ 15 = 4
Urgent 1111 needs a process

Multiply both sides of the equation by 75 at the same time
3X+5X=300
8X=300
X=300÷8
X=37.5

If the tangent slope of the function y = x ^ 2 + 4x at x = x0 is 2, then x0 =, the final simplified formula of the answer is 2x0 + 4, and the solution is x0 = - 1. But in my process, there is always one more Δ X. mine is 2x0 + 4 + Δ X
By the way, it's the same with limit operation. This Δ x doesn't take into account

y'=2x+4
y'(x0)=2x0+4=2
x0=-1

In rational numbers. The number that is an integer but not a positive number is______ A number that is an integer and not a negative number is______ ．

Zero is neither a positive number nor a negative number, so in rational numbers, the numbers that are integers but not positive numbers are (0 and negative integers); the numbers that are integers but not negative numbers are: (0 and positive integers)

Given that the domain of F (2 ^ x) is [1,2], then the domain of y = f (Log1 / 2x) is [1,2]

For f (2 ^ x)
Let t = 2 ^ X
The domain is [1,2]
Then t belongs to [2,4]
That is, the domain of F (T) is [2,4]
So for y = f (Log1 / 2x)
log1/2x∈[2,4]
Then (1 / 2) ^ 4 ≤ x ≤ (1 / 2) ^ 2
Namely:
1/16≤x≤1/4

The reciprocal of 2 / 3 and the sum of 9 / 4 are more than 1 / 2 of a number. What is the number?

Let this number be X
The reciprocal of 2 / 3 = 3 / 2
Then 3 / 2 + 9 / 4-2 = 1 / 2 times X
The solution is x = 7 / 2
This number is seven out of two

To solve the system of linear equations of three variables: 5x + y + Z = 1 (1) 2x-y + 2Z = 1 (2) x + 5y-z = - 4 (3)
To solve the linear equations of three variables
5x+y+z=1(1)
2x-y+2z=1(2)
x+5y-z=-4(3)

① + 3: 6x + 6y = - 3, get 2x + 2Y = - 1, 4
①*2-②:8x+3y=1,⑤
④ * 4 - ⑤: 5Y = - 5, y = - 1
Substituting into 4: x = (- 1-2y) / 2 = 1 / 2
Substituting ①: z = 1-y-5x = 1 + 1-5 / 2 = - 1 / 2
The solution is x = 1 / 2, y = - 1, z = - 1 / 2

Write out an interval of zero point of a positive number of function f (x) = X3 + 2x2-3x-6

F (x) = (x + 2) (x ^ 2-3) = (x + 2) (x + radical 3) (x-radical 3)
So zero is - 2, root 3, - root 3
The zero point of a positive number is the root 3
I don't know what grade you are. Why should you write the interval if you can work out the specific number?
Haven't you learned irrational numbers yet? If so, write (1,2)

How to know that there are two points of intersection between parabola and X axis

The parabola is y = ax & # 178; + BX + C
Calculate B & # 178; - 4ac,
If the value is greater than 0, there are two points of intersection with the X axis
If this value is equal to 0, there is a point of intersection with the X axis
If the value is less than 0, there is no intersection with the X axis