If the function f (x) = x ^ 3-4x ^ 2-ax + 3 is a monotone function in [1,2], find the value range of A

If the function f (x) = x ^ 3-4x ^ 2-ax + 3 is a monotone function in [1,2], find the value range of A

If f '(x) = 3x-8x-a, monotone on [1,2], then TA > = 0,64 + 3A > = 0, a > - 64 / 3
The second year of senior high school is not required, but the examination is in the back. Is that the question for the college entrance examination?

Given curve A: y = x ^ 2
B:y=-(x-2)^2
The line L is tangent to both a and B. The equation for finding l? The answer is y = 0 or y = 0
y=4x-4

Because a: y '= 2x
So: the tangent equation passing through a point (x0, Y0) on curve A is y-y0 = 2x0 (x-x0) and Y0 = x0 ^ 2
By y-y0 = 2x0 (x-x0) and y = - (X-2) ^ 2
Get: x ^ 2 + (2x0-4) x + 4-x0 ^ 2 = 0
Let Δ = 0
X0 = 0 or 2
When x0 = 0, the tangent equation is y = 0
When x0 = 2, the tangent equation is y-4 = 4 (X-2), that is y = 4x-4
To sum up, the tangent equations of a and B are as follows:
Y = 0 or
y=4x-4

The fuel cost of a ship is directly proportional to the square of the ship's speed. If the ship's speed is 10km / h, the fuel cost per hour is 80 yuan. It is known that the other costs of a ship's voyage are 480 yuan / h. what is the speed in a 20km voyage, and the total cost is the least?

Let fuel cost be y and ship speed be X
Then y = KX ^ 2
When x = 10, y = 80, so k = 0.8
Total cost = (20 / x) * 0.8x ^ 2 + 20 / X * 480
=16X+9600/X
=16(√X-√60/√X)^2+16*2√60
>=32√60
Therefore, when the ship speed x = √ 60, the total cost is at least 32 √ 60

Five math problems of Liberal Arts in senior three. Derivative and its application
1. If f (x) = x ^ 2 + 2x f '(1), then f' (0)=____
2. Given the function f (x) = g (x) + x ^ 2, the tangent equation of curve g (x) at point (1, G (1)) is y = 2x + 1, then the tangent slope of curve y = f (x) at point (1, f (1)) is y = 2x + 1_____
3. Of all rectangles with area s (fixed value), the perimeter of the rectangle with the smallest perimeter C is____
4. On the curve y = - x ^ 2 + 4 (x > 0), the coordinates of the point closest to the fixed point P (0,2) are_____
5. If the area of the triangle formed by the tangent of the curve y = x ^ 3 at the point (a, a ^ 3) (a ≠ 0) and the X axis and the straight line x = a is 1 / 6, then a=_____
Please write the process, thank you

1. Take the derivative f '(x) = 2x + 2F' (1) on both sides of the equation
When x = 1, f '(1) = 2 + 2F' (1)
So f '(1) = - 2, f' (x) = 2x - 4
So f '(0) = - 4
2.f'(x)=g'(x)+2x
Because the tangent equation of curve g (x) at point (1, G (1)) is y = 2x + 1
So G '(1) = 2
So f '(1) = g' (1) + 2x1 = 4. That is to say, the slope of the tangent of = f (x) at point (1, f (1)) is__ 4__
3. Using derivative method
Let length a, then width s / A
Perimeter y = 2 (a + S / a)
Y '= 2-2s / A ^ 2 = 0. When a = sqrt (s), y is the smallest
And Ymin = 2 * 2sqrt (s)
4. Let the point coordinate a (x, - x ^ 2 + 4), P (0,2)
So the slope of AP is (- x ^ 2 + 4-2) / (x-0) = - x + 2 / X
y'=-2x
Because of the shortest distance, the tangent is perpendicular to the AP line, so the slope product is (- 1)
So (- 2x) (- x + 2 / x) = 2x ^ 2-4 = - 1
So x = - √ 6 / 2
So (- √ 6 / 2,5 / 2)
5. Tangent k = 3x ^ 2 = 3A ^ 2
Let x = a ^ 3 / k = A / 3 the distance between the focus of tangent and X axis and (a, 0)
S=a/3×a^3×1/2=1/6
So a = 1 or - 1
It's hard to write!

Given the set a = {x x + X-6}, B = {x 12 + x-x ＞ 0}, C = {x-4ax + 3a ＜ 0}, find (1) a ∩ B (2) if C (a ∩ b), try to determine the value range of real number a

A = {x ｜ x + X-6} greater than 0 or less than 0? Write clearly