If a and B are known to be real constants, then f (x) = a | X-B | + 2 is an increasing function in the interval [0, positive infinity], if and only if

If a and B are known to be real constants, then f (x) = a | X-B | + 2 is an increasing function in the interval [0, positive infinity], if and only if

a>0,b0,b

Given the cube of function f (x) = 3 + the square of AX + BX + C (a, B, C are all constants), the tangent of curve y = f (x) at point x = 1 is 3x-x + 1 = 0, if x = 2, y = f (x) has extremum, find the value of a, B, C, find the maximum and minimum value of y = f (x) on [- 3,1]

F '(x) = 3x & # 178; + 2aX + B has extremum at x = - 1, so f' (- 1) = 03-2a + B = 0g '(x) = 8x-7x = 2 has common tangent, so the slope is equal, that is, the derivative is equal, so f' (2) = g '(2) 12 + 4A + B = 94A + B = - 3, so a = 0, B = - 3f (x) = x & # 179; - 3x + C passes (2,4) f (2) = 48-6 + C = 4C = 2, so a = 0, B = - 3, C = 2

The sufficient and necessary condition of "function f (x) = Tan (x + φ) is odd function" is "φ = KX (K ∈ z)". What's wrong with this proposition?
The sufficient and necessary condition of "function f (x) = Tan (x + φ) is odd function" is "φ = k Π (K ∈ z)"

For example, when φ = Pi, we can deduce that it is an odd function

If (x ^ m ／ x ^ 2n) ^ 3 ／ x ^ (m-n) and - 1 / 3x ^ 2 are of the same kind, and 2m + 5N = 6. Find the square root of 4m ^ 2-25n ^ 2

(x^m÷x^2n)^3÷x^(m-n)
=[x^(m-2n)]^3÷x^(m-n)
=x^[3(m-2n)-(m-n)]
=x^(2m-5n)
If x is of the same kind, then x has the same degree
So 2m-5n = 2
And 2m + 5N = 6
So 4m ^ 2-25n ^ 2 = (2m + 5N) (2m-5n) = 2 * 6 = 12

What is the difference between y = log2 (x2-1) and y = log2 (x2 + 1)
There are also y = log2 (1 / x-1) and y = log2 (x / x-1) value range and differences

【1】 Y = log (2) [x & # 178; - 1] function definition field is: X & # 178; - 1 > 0, get: x > 1 or x0, so the value range of this function is r [2]. Similarly, let: T = x & # 178; + 1, then: t ∈ [1, + ∞) get: y = log (2) [t], where, t ∈ [1, + ∞) get: y ∈ [0, + ∞) [3] y = log (2) [1 / (x-1

What is the minimum value of the function f (x) = SiNx cosx ^ 2?

SiNx cosx ^ 2 = SiNx - (1-sinx ^ 2) = SiNx ^ 2 + sinx-1 if SiNx is regarded as an independent variable, the axis of symmetry is - 1 / 2
-1 < SiNx < 1, so the axis of symmetry is in the domain of definition, so the minimum value is the value at the axis of symmetry
The minimum value of F (x) is (- 1 / 2) ^ 2-1 / 2-1 = - 5 / 4

Given that the two zeros of the function f (x) = x ^ 2 + BX + C are - 1 and 2 respectively, the solution set of the inequality | X-3B | > - 2C is?

That is, the root of X & sup2; + BX + C = 0 is - 1,2
Weida theorem
-1+2=-b,
-1*2=c
b=-1,c=-2
So the inequality is | x + 3 | > 4
x+34
x1

Let a and B be symmetric matrices of order n, and prove that AB is symmetric if and only if AB = ba

It is necessary to prove that a and B are all positive definite matrices of order n. according to the definition of positive definite matrix, a and B are symmetric matrices of order n, that is, a '= a, B' = B (where a 'denotes transpose matrix of a). If AB is positive definite, then AB is also symmetric matrix, so AB = (AB)' = b'a '= ba. That is to say, ab = Ba is proved, Note that p'pq'q = q ^ (- 1) (qp'pq ') Q, which shows that p'pq'q is similar to (qp'pq'). In addition, qp'pq '= (PQ') '(PQ'), according to P and Q are invertible real matrices, PQ 'is also invertible real matrix, so qp'pq' is positive definite, so the eigenvalues of qp'pq 'are positive real numbers, So the eigenvalues of AB = p'pq'q are all positive real numbers

List some common English nouns with the same singular and plural

The following nouns are in the same form: fish, deer, deer, sheep, works, means, Swiss, Swiss, Chinese. The Chinese only have plural nouns: trousers, pants, shorts, glasses, compasses, compasses, scales, pliers, pliers, C

Simple calculation of 1 + 1 × 2 + 8 × 5

1x(1+2)+8x5
=1x3+8x5
=3+40
=43