Let f (x) = A / 3x3-3 / 2x2 + (a + 1) x + 1, where a is a real number (1) Let f (x) obtain the extremum at x = 1 and find the value of a; (2) Let f '(x) > x2-x-a + 1 hold for any a ∈ (0, + ∞), and find the value range of real number X Second, how to move items and merge.

Let f (x) = A / 3x3-3 / 2x2 + (a + 1) x + 1, where a is a real number (1) Let f (x) obtain the extremum at x = 1 and find the value of a; (2) Let f '(x) > x2-x-a + 1 hold for any a ∈ (0, + ∞), and find the value range of real number X Second, how to move items and merge.

Let f '(x) = x Λ 2-3x + 2, let H (x) = f' (x) - [x Λ 2-x-a + 1] = 2x - (1 + a) let H (x) = 0, then x = 0.5 (1 + a) and a ∈ (0, ∞) so x ∈ (- ∞, 0.5]

Given the function f (x) = a3x3 − a + 12x2 + X + B, where a, B ∈ R. (I) if the tangent equation of curve y = f (x) at point P (2, f (2)) is y = 5x-4, find the analytic expression of function f (x); (II) when a > 0, discuss the monotonicity of function f (x)

(I) f '(x) = AX2 - (a + 1) x + 1, from the geometric meaning of derivative, f' (2) = 5, then a = 3. From the tangent point P (2, f (2)) on the straight line y = 5x-4, we know 2 + B = 6, and the solution is b = 4. So the analytic expression of function f (x) is f (x) = x3-2x2 + X + 4. (II) f '(x) = AX2 − (a + 1) x + 1 = a (x − 1a) (x − 1). When 0 < a < 1, 1A > 1, the function f (x) is in the interval (- ∞, 1) and (1a) When a = 1, 1A = 1, f (x) is an increasing function in the interval (- ∞, + ∞); when a > 1, 1A < 1, f (x) is an increasing function in the interval (− & nbsp; ∞, 1a) and (1, + ∞), and is a decreasing function in the interval (1a, 1)

In a hurry
The stationery store bought some erasers, 10 yuan per box, 4.4 yuan per box, retail price 0.6 yuan per box, pencil 1.3 yuan per bundle. The stationery store sold 28 erasers and 15 pencils in one day. How much did the erasers and pencils make on that day

The purchase price of rubber is 4.4/10 = 0.44 yuan
6-0.44 = 0.16 yuan
Rubber profit 0.16 × 28 = 4.48 yuan
Please add a question about the unclear expression of pencil

How to judge a + B + C in quadratic function
2a+b
4a-2b+c
a-b+c
4a+2b+c
c-a
How to judge whether there are other forms

Because the analytic expression of quadratic function is y = ax ^ 2 + BX + C, when the value of X is 1, y is equal to a + B + C, and then you look at the image. When the value of X is 1, is the corresponding value of Y on the positive half axis or negative half axis of Y. if it is on the positive half axis, that is, y is greater than 0, it is a + B + C > 0. If it is on the negative half axis, that is, y is less than 0, it is a + B + C < 0
We must draw and analyze, and cultivate the thought of combination of number and shape

Given x + y = xy = 4, find the fourth power of X + the fourth power of Y, the eighth power of X + the eighth power of Y

x=y=2
The fourth power of X + the fourth power of y = the fourth power of 2 + the fourth power of 2 = 16 + 16 = 32
The eighth power of X + the eighth power of y = the eighth power of 2 + the eighth power of 2 = 256 + 256 = 512

Given cos (x + y) = 1 / 3, cos (X-Y) = 1 / 5, find the value of TaNx × tany

-1/4

Fill in the circle with the appropriate operation symbol and the box with the appropriate number to make the equation 79 + 79 * 9 = Box * (box circle box)
Use words instead

Is 79 + 79 * 9 = 79 (1 + 9) like this

As shown in the figure, in △ ABC, the bisector of ∠ B and ∠ C educates point P. let ∠ a = x ° and ∠ BPC = y ° and find the functional relationship between Y and X when ∠ a changes
As shown in the figure, in △ ABC, the bisector of ∠ B and ∠ C educates point P, let ∠ a = x °, BPC = y ° and find the functional relationship between Y and X when ∠ a changes, judge whether y and X are first-order functions of X, and point out the value range of independent variable

It is also known that: a + B + C = 180 ° i.e. x °+ ∠ B + C = 180 °, B + C = 180 ° - x ° because BP and CP are the bisectors of angle B and angle c, so ∠ PBC + PCB = 1 / 2 (∠ B + C) because: BPC + PBC + PCB = 180 °
So ∠ BPC + 1 / 2 (∠ B + ∠ C) = 180 ° i.e. y ° + 1 / 2 (180 ° - x °) = 180 °
It is concluded that y ° = 1 / 2x ° + 90 ° y is a linear function of X because 0

If you travel 50 kilometers per hour from a to B, you will be 15 minutes late. If you travel 60 kilometers per hour, you will arrive 15 minutes early. How many hours do you plan to arrive from a to B?

15 minutes = 0.25 hours
(50 * 0.25 + 60 * 0.25) / (60-10) = 2.75 hours
Distance divided by speed equals time

Given the curve y = (x-3 / 4) ^ 2 and the straight line L: y = KX, if there are two symmetric points about L on the curve C, find the range of K
In the second problem, we know that there are two points AB on the ellipse C: 3x ^ 2 + 4Y ^ 2 = 12, which are symmetric with respect to the straight line y = 4x + 1 / 2, so we can find the AB linear equation
Can we have a process

If two symmetric points are a (x1, Y1) B (X2, Y2), then the slope of the straight line AB = - 1 / k = (y1-y2) / (x1-x2) and the point ((x1 + x2) / 2, (Y1 + Y2) / 2) is on y = kx, then: Y1 = (x1-3 / 4) ^ 2Y2 = (x2-3 / 4) ^ 2 subtracting (y1-y2) = (x1-x2) (x1 + x2-3 / 2) - 1 / k = (x1 + x2-3 / 2) X1 + x2 = 3 / 2-1 / K substituting y = k