The tangent equation of curve f (x) = [f '(1) / E] * e ^ x-f (0) x + 1 / 2 (x ^ 2) at point (1, f (1)) is

The tangent equation of curve f (x) = [f '(1) / E] * e ^ x-f (0) x + 1 / 2 (x ^ 2) at point (1, f (1)) is

F (x) = [f '(1) / E] * e ^ x-f (0) x + 1 / 2 (x ^ 2) let x = 0, then f (0) = f' (1) / EF '(1) = ef (0) let x = 1, then f (1) = f' (1) - f (0) + 1 / 2 = ef (0) - f (0) + 1 / 2, then f '(x) = [f' (1) / E] * e ^ x-f (0) + X let x = 1, then f '(1) = f' (1) - f (0) + 1F 1, so f '(1) = ef (1)

If the tangent of the curve f (x) = x3-x2 at point P is parallel to y = x, find the equation of the tangent

F (x) = x3-x2, so f '(x) = 3x ^ 2-2x
The tangent at point P is parallel to y = x, that is, the slope k = 1
3x ^ 2-2x = 1, the solution is x = 1 or - 1 / 3
Substituting the two values into f (x) = x3-x2, the two tangent points are (1,0), (- 1 / 3, - 4 / 27)
So the tangent equation is: x-y-1 = 0
Or 27x-27y + 5 = 0
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The equation of tangent of curve y = X3 + x2-1 at point m (1,1) is______ ．

∵ curve y = X3 + x2-1, ∵ y ′ = 3x2 + 2x, when x = 1, y ′ = 5, ∵ tangent equation is Y-1 = 5 (x-1), that is, 5x-y-4 = 0

Find the tangent equation of curve y = f (x) = X3 + 2x-1 at point P (1,2)
Detailed steps should be taken

∵y=f(x)=x³+2x-1
∴y′=f′(x)=3x²+2
That is, the slope of tangent k = 5
The tangent equation is: (Y-2) = 5 (x-1)
That is: 5x-y-3 = 0

Try to determine the constants a, B, C, D in the curve y = ax ^ (3) + BX ^ (2) + CX + D, such that x = - 2 is the stationary point, points (1, - 10) are the inflection points, and the curve passes through points (- 2,44)

y'=3ax^2+2bx+c
y"=6ax+2b
Points (1, - 10) are inflection points
So 0 = 6A + 2B
X = - 2 is the stationary point
So 12a-4b + C = 0
Curves passing (1, - 10) and (- 2,44)
-10=a+b+c+d
44=-8a+4b-2c+d
a=1,b=-3,c=-24,d=16

Try to determine a, B, C, D in the curve y = ax ^ 3 + BX ^ 2 + CX + D, so that the tangent of the curve at x = - 2 is horizontal, the point (1, - 10) is the inflection point, and the point (- 2,44) is on the curve

According to the meaning (1, - 10) and (- 2,44) are on the curve
a+b+c+d=-10
-8a+4b-2c+d=44
The tangent formula of the curve is y = 3ax ^ 2 + 2bx + C, and the tangent is horizontal, that is 12a-4b + C = 0
The second derivative 6AX + 2B = 0 is defined by the inflection point, that is, 6a + 2B = 0
A = 1, B = - 3, C = - 24, d = 16

Magic square of order 25 with center 1

The method is very simple: 1. Put it in the center grid and walk the horse step. If there are already numbers in the drop grid, go back one grid and fill in the magic square. My magic square document has a ready-made screenshot for you. Magic sum value, f (n) = n (n ^ 2 + 1) / 2 = 25 × (25 ^ 2 + 1) / 2 = 25 × (625 + 1) / 2 = 7825. Ask questions

Making a magic square of order 4 from 10 to 25 with symmetry method

First of all, I will tell you how to make a magic square of order 4 with 1-16. The method of making a magic square of order 4 is two sentences: fill in the numbers in order, and exchange the numbers symmetrically with the center point. The first step is to put 1 in any corner of the four corners of the magic square of order 4, and fill in the remainder in order in the same direction. As follows: 1234567891011121314

Write a magic square of order 41 according to Roberts method

It's very troublesome and meaningless to fill in magic square of such a large order directly with Rob's method
It is as like as two peas in natural array transformation.
1. Arrange natural number matrix. It's easy to complete with spreadsheet
2. The middle row of the natural number matrix does not move, and the upper row moves to the right 1, 2, 3 from bottom to top The following lines move left from top to bottom by 1, 2, 3 20 squares; the translation complement of magic box
3. Move the middle column of the changed matrix, and move the left column down 1, 2, 3 from right to left The columns on the right side move up 1, 2, 3 from left to right The magic square constructed by Roberts method can be completed

Nine level cube
Yongjun 9 level 600 is not expensive?

Rubik's cube beyond a certain order will lose its meaning and become a simple complex. It has been a meaningless breakthrough. There are 11 orders. Is it meaningful? I suggest you buy a special-shaped Rubik's cube