Find the maximum and minimum of the square of function f (x) = x - 2mx + m on [1, - 1]

Find the maximum and minimum of the square of function f (x) = x - 2mx + m on [1, - 1]

discuss
Quadratic function with function opening upward
When the symmetry axis is m > 1 on the right side of x = 1, that is, the maximum value is f (- 1) and the minimum value is f (1), it can be seen from the drawing
The axis of symmetry is m to the left of x = - 1

F (x) = the minimum value of the square of x-2mx-1 in [0.4]

First of all, the position of the symmetry axis of the half segment must be determined. The symmetry axis X = - B / 2A = M
So there are three situations to discuss
1. When the axis of symmetry is on the left side of [0.4], m ＜ 0, it is an increasing function in [0.4] because a > 0 and the opening of the function is upward
When x is 0, the minimum is y = - 1
2. When the symmetry axis is in the middle of [0.4], 0 ＜ = m ＜ = 4, when x is equal to the symmetry axis, the minimum x = m, the minimum y = - m ^ 2-1
3. When the symmetry axis is on the right side of [0.4], when m > 4, it is a decreasing function on [0.4], and when x is 4, the minimum value is y = 15-8m

Solve the answer of "Let f (x) = the square of X - 2mx + 1, find the minimum value of function f (x) on [0,4]"

f(x)=x^2-2mx+1
f'(x)=2x-2m＝2（x-m）
Let f '(x) = 0, x = M,
Discussion:
1) If M > 0, then f '(x) > 0, then f (x) increases monotonically, and the minimum value is f (0) = 1
2) If 0

Find the integer solution of equation, 11x + 16y = 3
This is an infinitive equation

X=9,y=-6

When m is a value, the solution of the equation 5m + 12x = 4 + 11x is 2 times larger than that of the equation x (M + 1) = m (1 + x)

5m+12x=4+11x
x=4-5m
x（m+1）=m（1+x)
(m+1)x=m+mx
(m+1-m)x=m
x=m
Big 2
4-5m-m=2
m=1/3

How to solve the equation of 5 * 11x-10) / (11x) = (5 * 7x + 10) / (7x + 4) is explained step by step

（5*11X-10）/(11X)=（5*7X+10）/（7X+4)
By cross multiplication, we get 385x2 + 220-70x-40 = 385x2 + 110x
220-40 =110x+70x
180x=180
x=1
If the test is consistent with the meaning of the question, then x = 1

We know that parabola y ^ 2 = 4x, ellipse x ^ 2 / 9 + y ^ 2 / M = 1, they have the same focus F2
Finding the value of M
If P is a common point of two curves and F1 is another focus of ellipse, calculate the area of angle pf1f2

The focus of the parabola is (1,0)
c^2=a^2-b^2
c^2=9-m
Because C = 1, M = 8
Connect the two equations y ^ 4 + 18y ^ 2 = 144
The result is y F1F2 = 2C = 2
Area s = 2 * | y | * 1 / 2 = | y|

It is known that the parabola y ^ 2 = 4x, the ellipse x ^ 2 / 9 + y ^ 2 / M = 1, they have a common focus F2, the other focus of the ellipse is F1, and the point P is the intersection of the parabola and the ellipse in the first quadrant. Find the product of COS angle pf1f2 and COS angle pf2f1

Obviously, we can get: F2 (1,0) so C = 1, and the focus is on the X axis, so a = 3, so m = 8. Obviously, we can get x = - 1 of the parabola, and calculate the P coordinate (3 / 2, root 6), so we can get PF2 = P, the distance from the parabola to the parabola is d = 2.5. According to the first law of ellipse, we can get Pf1 = 2a-d = 3.5 and F1F2 = 2C = 2

Let m = {x | X & # 178; - 4x < 0, X ∈ r}, n = {x | x | 4, X ∈ r}, then
A M∪N＝M
B M∩N＝M
I can't get the rest. How much is it

Choose B, M: 0

Given that 2 + 3 is a root of the quadratic equation x2-4x + M = 0, then the other root of the equation is______ ，m=______ ．

∵ 2 + 3 is a root of the univariate quadratic equation x2-4x + M = 0, ∵ X1 + x2 = 4, then the other root of the equation is: 2 + 3 + x2 = 4, ∵ x2 = 2-3; ∵ M = x1x2 = (2 + 3) (2-3) = 4-3 = 1