What is the minimum value of function y = [x-4] + [X-6]

What is the minimum value of function y = [x-4] + [X-6]

y=|x-4|+|x-6|
=|x-4|+|6-x|≥|x-4+6-x|=|2|=2
So the minimum value is 2
With the method of zero point segmentation, the discussion is classified. The minimum is 2
Analysis: the minimum value of y = [x-4] + [X-6] is the sum of the distances from one point on the X axis to 4, 0 and 6, 0
It's the smallest point between 4, 0 and 6, 0
Ymin = [x-4] + [X-6] = 6-4 = 2
2. Y represents the distance from a certain point to 4 on the number axis plus the distance from this point to 6. It must be the minimum distance when this point is between 4 and 6. At this time, y = 2
When x = [5], y is the smallest
The function y = the square of negative x plus the absolute value of X, the monotone decreasing interval is, the maximum value and the minimum value are
The absolute value of the square of function y = - x + X, the maximum and minimum are
f(x)=-x^2+|x|
Classified discussion
When x ≥ 0
f(x)=-x^2+x
=-(x-1/2)^2+1/4
Maximum f (1 / 2) = 1 / 4
No minimum
When x
Minimum: 0 (x = 0)
Maximum: Infinity (x infinity)
Because (- x) squared > = 0, | x | > = 0
Given that the maximum value of F (x) = | x | - SiNx + 1 | x | + 1 (x ∈ R) is m and the minimum value is m, then M + M = M___ .
The function f (x) can be transformed into f (x) = 1 + - SiNx | - SiNx | - sinx-sinx | + 1, let g (x) = - SiNx | - SiNx + 1, then G (- x) = SiNx | - SiNx | - SiNx + 1 | - SiNx + 1 | - SiNx + 1 | - x | | + 1 | (x | \124\\\\\\\\\\\124\\\\\\\\\\\thereis a minimum of - G (a) + 1 M = g (a) + 1, M = - G (a) + 1, M + M = 2, so the answer is 2
Let f (x) = | SiNx + 2 / (3 + SiNx) + m | (x belongs to R, m belongs to R) be g (x), then what is the minimum value of G (x)
The answer seems to be 3 / 4
See below:
Let f (x) = | SiNx + 2 / (3 + SiNx) + m | (x belongs to R, m belongs to R) be g (m), then what is the minimum value of G (m)
F (x) = | SiNx + 2 / (3 + SiNx) + m | = | (SiNx + 3) + 2 / (3 + SiNx) + M-3 | because - 1 ≤ SiNx ≤ 1, so 2 ≤ SiNx + 3 ≤ 4, it is easy to prove that the function y = x + 2 / X monotonically decreases on (0, √ 2] and monotonically increases on [√ 2, + ∞), so the minimum value of (SiNx + 3) + 2 / (3 + SiNx) is 2 + 2 / 2 = 3, and the maximum value is 4 + 2 / 4 =
Is it just a denominator and a numerator?
2 / radical 3 × Tan 60 ° - 2 / radical 2 × cos 45 ° =?
simple form
=2/√3×√3-2/√2×√2/2
=2-1
=1
tan60°=√3 cos45=√2/2
Substitute for 1
How to prove that a square matrix of order n with rank 1 can be written as an n-dimensional column vector multiplied by an n-dimensional row vector
Very simple, since the rank of matrix A is 1, it must be transformed into diag (1,0,0,. 0) form by elementary transformation
Let the transformation matrix be p, Q, then
PAQ = diag(1,0,...,0)
A = p'diag (1,0,..., 0) Q '(p', q 'denotes the inverse matrix of P, q)
=P' diag(1,0,...,0) diag(1,0,0...,0) Q'
P'diag (1,0,..., 0) is equal to a matrix which is 0 except the first column which is not 0
Diag (1,0,..., 0) Q 'is equal to a matrix with all zeros except the first row which is not zero
The product of these two matrices is equivalent to the first column of p'diag (1,0,..., 0) multiplied by the first row of diag (1,0,..., 0) Q '
Get proof
If the coordinates of the three vertices of △ ABC are a (4,1), B (2,3), C (9, - 3), and the median line parallel to AB is Mn, then the equation of the straight line Mn is
The slope of line Mn is equal to that of line ab
So the slope of Mn = (3-1) / (2-4) = - 1
The midpoint of AC is (13 / 2, - 1)
So Mn: y + 1 = - (X-13 / 2), that is, 2x + 2y-11 = 0
Mn slope (3-1) / (2-4) = - 1
AB intercept y = - x + 5
C / / AB intercept y = - x + 6
5 Mn intercept
Mn equation y = - x + 5.5
Given LIM (3an + BN) = 8, LIM (6An BN) = 1, find LIM (an * BN)
Let LIM (3an + BN) = 8 (1)
lim（6An-Bn）=1 …… II.
① The solution is LIM (9An) = 9 and lim (an) = 1;
① X2 - 2 gives LIM (3bn) = 15 and lim (BN) = 5;
The solution is wrong, so the undetermined coefficient method is used,
Let 3an + BN = CN, 6An BN = DN, then Lim CN = 8, Lim DN = 1An = (CN + DN) / 9bn = (2cn DN) / 3lim (an * BN) = Lim [(CN + DN) / 9 * (2cn DN) / 3] = 5, which is the correct solution
Who accused you of being wrong? Theorem 3 on page 43 of Tongji 5th Edition
provided that
limf（x）=A
limg（x）=B
Then limf (x) g (x) = limf (x) limg (x) = ab
Let x = 3an + BN, y = 6An BN
Then, the formula is: 2x-y = 2 (3an + BN) - (6An BN) = 3bn, that is, BN = (2x-y) / 3
X + y = (3an + BN) + (6An BN) = 9An, that is, an = (x + y) / 9
So LIM (an * BN) = Lim [(2x-y) / 3] * [(x + y) / 9]
=lim（（2*8-1）/5）（（8+1）/9）
=5
Calculation: root 14 + 6 root 5 - root 14 - 6 root 5
√14＋6√5－√14－6√5=0