The image c of function f (x) = x ^ 3 + ax ^ 2 + BX is tangent to the X axis at a point different from the origin, and the minimum value of F (x) is - 4. Find the analytic expression and monotone interval of function f (x)

The image c of function f (x) = x ^ 3 + ax ^ 2 + BX is tangent to the X axis at a point different from the origin, and the minimum value of F (x) is - 4. Find the analytic expression and monotone interval of function f (x)

F (0) = 0, and because the minimum is - 4 and tangent to the X axis, the tangent point is not at the origin. Therefore, the drawing shows that the tangent point is on the left side of the origin and is the maximum of the function. F (x) '= 3x ^ 2 + 2aX + B = 0 has two solutions, one is the tangent point and the maximum (x0,0), the other is the minimum (x1, - 4) x0 3x1 + 3x0 + 2A = 02x0 ^ 2 + ax0

The basic properties of subtraction

1. A certain number minus a certain number, plus the same number, a certain number remains unchanged, that is, (a-b) + B = A.2. A certain number plus a certain number, minus the same number, a certain number remains unchanged, that is, (a + b) - B = A.3. The sum of N numbers minus a certain number, can be subtracted from any addend (if it can be subtracted), and then be the same as

If SiNx = 2cosx, then 1 + SiNx ^ 2 =?

sinx=2cosx
tanx=2
1+(sinx)^2=1+1-(cosx)^2=2-1/(secx)^2=2-1/((tanx)^2+1)=2-1/(2^2+1)=2-1/5=9/5

What is abdication addition and subtraction method in grade one of primary school

For example, 23-9 digits, 3-9, are not enough
So borrow one from two, which is ten digits
Now it's 13-9
But the original ten digit 2 becomes 1, because it is borrowed one, so it is less 1,2-1 = 1
13－9＝4
So 23-9 = 14
Ten digits from the original 2 into 1, back one, so it is called abdication plus minus method
For example, 29-7 = 22
9 is bigger than 7, so you don't need to borrow. So it's not abdication plus minus

On the equations of X, y, the solution of formula (1) 2x + y = 3, formula (2) x + 2Y = 9-3a satisfies x + y < A, and the range of a is obtained

"Formula 1 + 2 gives 3x + 3Y = 12-3a, so x + y = 4-a

1 2 3 4 5 6 make a formula to make a two digit number multiplied by a number equal to a three digit number, and the number shall not be repeated

54 times 3 = 162

If the hyperbola y = K / X passes through point a (2,2) and point B (4, m), then the area of △ AOB is______ ?
Trouble problem-solving process to write more detailed... Personal I did not understand

Substituting point a (2,2) into y = K / x, we can get: 2 = K / 2, k = 4  y = 4 / X; substituting point B (4, m) into y = 4 / x, we can get: M = 1, that is, B (4,1) straight line ob slope k = 1 / 4, the linear equation is Y-1 = (1 / 4) * (x-4), x-4y = 0, the distance between point a and straight line ob is d = / 2-4 * 2 / / √ [1 ^ 2 + (- 4) ^ 2] = 6 * (√ 17) / 17 (/ 2-4 * 2 / is (2-4 * 2)

-What is 1 + 6 / 5-12 / 7 + 20 / 9-11 / 30 + 13 / 42-15 / 56 + 17 / 72?

=-1+(1/2+1/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)+(1/8+1/9)
=-1+1/2+1/9
=11/18

On the equation of X (a + C) x ^ 2 + BX - (2c-a) = 0, the sum of the two is - 1, and the difference between the two is 1

Two roots x1, x2
x1+x2=-1
x1-x2=1
x1=0,x2=-1
The equation is as follows
(a+c)x(x+1)=0
=>
a+c=b
2c-a=0
=>
a:b:c=2:3:1

Is the mathematical formula calculated first, multiplication and division followed by addition and subtraction

Mathematical formula also follows the principle of counting, multiplying and dividing before adding and subtracting