Let f (x) = ax ^ 3 + BX ^ 2 + CX + 12, the intersection of the image and the Y axis be p, and the curve has the tangent equation 24x + Y-12 at P, and the extreme value of the function is - 16 at x = 2, Find the monotone decreasing interval of the function

Let f (x) = ax ^ 3 + BX ^ 2 + CX + 12, the intersection of the image and the Y axis be p, and the curve has the tangent equation 24x + Y-12 at P, and the extreme value of the function is - 16 at x = 2, Find the monotone decreasing interval of the function

If f '(x) = 3ax ^ 2 + 2bx + C curve has tangent equation 24x + Y-12 = 0 at P point, the coordinates of P point can be obtained as follows: (0,12): F' (0) = C = - 24, the extremum at x = 2 is - 16, and 12A + 4B + C = 08A + 4B + 2C + 12 = - 16. In conclusion, the solution is a = 1, B = 3, so f '(x) = 3x ^ 2 + 6x-24 = 3 (X-2

For the cubic function f (x) = x ^ 3 + BX ^ 2 + CX + D, it can be seen from the graph that if there is an extreme value
For the cubic function f (x) = x ^ 3 + BX ^ 2 + CX + D, it can be seen from the graph that if there is an extremum, the extremum on the left must be a maximum point, and the extremum on the right must be a minimum point? Why? This rule is applicable to all cubic functions? There is also a quartic function. If there is only one stagnation point, it must be a minimum point. Why?

For the graph of cubic function, we can use the so-called method to draw
For a quartic function, it can be obtained that the derivative function is cubic and there is only one stationary point, which means that the derivative function has only one solution. If we study the cubic function again, we will know that the left side of the solution is less than 0 and the right side is greater than 0, so we get the minimum value at the stationary point

It is known that the function f (x) = X3 + bx2 + CX + 2 has extremum when x = 1. (I) find the value of B and C; (II) if the tangent of F (x) is parallel to the line 3x + y + 1 = 0, find the tangent equation

(I) f ′ (x) = 3x2 + 2bx + C, f (1) = 6, f ′ (1) = 0. We can get 1 + B + C + 2 = 63 + 2B + C = 0, B = - 6, C = 9. (II) from (I), we can know that f ′ (x) = 3x2-12x + 9, according to the meaning of the title, the slope of the tangent is - 3. Let f ′ (x) = 3, we can get x = 2, that is, f ′ (2) = 3

Taxis in a city charge 5 yuan for less than 3000 meters (including 3000 meters), and 1.2 yuan for every kilometer more than 3000 meters
If someone takes a taxi for X km (x > 3), he should pay____ If someone pays 12.2 yuan, he will take the bus____ Kilometers

1.2（x-3）=12.2-5
x-3=7.2÷1.2
x=6+3
X = 9 (km)

As shown in the figure, the ratio of length to width of a rectangular field ABCD is 2:1, de ⊥ AC at point E, BF ⊥ AC at point F, connecting be and DF
Reward score: 0 - settlement time: 2006-12-20 18:51
As shown in the figure, the ratio of length to width of a rectangular field ABCD is root sign 2:1, de ⊥ AC at point E, BF ⊥ AC at point F, connecting be and DF. It is planned to plant flowers and plants in the quadrilateral debf area, and calculate the area ratio of quadrilateral debf and rectangular ABCD

1. Find out that the length of AC is root 3
2. Prove AF = Fe = EC = root 3 / 3
3. According to Pythagorean theorem, BF = radical 6 / 3
4. According to the above conditions, the sum of the area of triangle BFE and triangle DFE (that is, the area of parallelogram debf) can be found to be 2 / 3 of the root
5. Find out the area of rectangle ABCD is root 2
The area ratio of quadrilateral debf to rectangle ABCD is 1:3

There are two kinds of pencils in the stationery shop, two pencils of type A and three pencils of type B. now it's 12 yuan. I bought 120 pencils. How many pencils do you buy for each of type A and B

Let a buy two of a and B buy three of B
｛2a+3b=120
｛0.3a+0.2b=12
a= 24
b=24
A 48, B 72

Party A, Party B and Party C have a total of 168 yuan. The first time Party A gives the same amount of money to Party B; the second time Party B gives the same amount of money to Party C; the third time Party C gives the same amount of money to Party A. at this time, the money of Party A, Party B and Party C is exactly the same?

The final amount of money per person is: 168 △ 3 = 56 (yuan); after the second time, a has: 56 △ 2 = 28 (yuan), C has: 56 + 28 = 84 (yuan), B has: 56 yuan; after the first time, C has: 84 △ 2 = 42 yuan, B has: 56 + 42 = 98 (yuan), a has: 28 yuan; then the original B has: 98 △ 2 = 49 (yuan

Given that there is an inscribed cube in the hemisphere, find the ratio of the volume of the hemisphere to the volume of the cube

Let the edge length of a cube be a, then the radius of the sphere is 2 / (2 ^ (1 / 2)) a
The volume of hemisphere is (2 / 3) pi * (2 / (2 ^ (1 / 2)) a) ^ 3
The volume of a cube is a ^ 3
Just compare yourself

The distance between the two places is 210 kilometers. A passenger train and a freight train leave from the two places at the same time. They meet in 3.5 hours. The passenger train runs 28 kilometers per hour. How many kilometers does the freight train run per hour?

Suppose that the freight car travels x kilometers per hour, 3.5 × 28 + 3.5x = 210, & nbsp; 98 + 3.5x-98 = 210-98, & nbsp; & nbsp; 3.5x △ 3.5 = 112 △ 3.5, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 32, a: the freight car travels 32 kilometers per hour

Practical problems of winter vacation in grade six of primary school
Car a and car B leave from two places at the same time. Car a runs the whole journey in 5 hours, and car B runs the whole journey in 4 hours. How many hours does car a and car B meet?
It takes 10 days for a project to be built by Party A and 18 days for team B. how many days does it take for the two teams to cooperate

1 / (1 / 5 + 1 / 4) = 20 / 9 (hours)
1 / (1 / 10 + 1 / 18) = 45 / 7 (hours)