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Known function f (x) = ln (MX) ²- If the definition field of 4mx + m + 3) is r, then the value range of real number M
almost done
It is known that the function f (x) = KX ^ 3-3 (K + 1) x ^ 2-k ^ 2 + 1 (k > 0), and the monotone decreasing interval of function f (x) is (0,4). When x > k, it is proved that 2 √ x > 3-1 / X
F '(x) = 3kx ^ - 6 (K + 1) x = 0, X1 = 0, X2 = 2 (K + 1) / K, k > 0, f (x) decreases on (x1, x2), and increases in other cases. It is known that the monotonic reduction interval of F (x) is (0,4), х 2 (K + 1) / k = 4, K + 1 = 2K, k = 1. F (x) = x ^ 3-6x ^ 2, when x > k = 1, 2 √ x > 3-1 / x, ① square is 4x > 9-6 / x + 1 / x ^ 2,4x ^ 3 > 9x ^ 2-6x + 1,4x
The function f (x0 = x ^ 2 + 2x + 3) is known. When x ∈ [- 2,2] is, G (x) = f (x) - KX is a monotone function, then the value range of K is
When x ∈ [- 2,2], G (x) = f (x) - KX = X ²＋ (2-k) x + 3, since g (x) is monotonic in [- 2,2], the axis of symmetry of G (x) should be outside this interval, that is:
|－(2－k)/2|≥2
|k－2|≥4
Obtained: K ≥ 6 or K ≤ - 2
Given the function f (x) = x2 + 2x + 3, when x ∈ [- 2,2], G (x) = f (x) - KX is a decreasing function, find the value range of real number K
From the title, there is g (x) = x ^ 2 + 2x + 3-kx
=x^2+(2-k)x+3
=[x+(2-k)/2]^2+3-(2-k)^2/4
Because the image of G (x) is a parabola with an upward opening, and when x ∈ [- 2,2], it is a subtractive function
That is, its axis of symmetry - (2-k) / 2 ≥ 2
That is, K / 2-1 ≥ 2
The solution is k ≥ 6
If the value of function y = KX + B is greater than the value of function y = - 2x + 2, find the value range of X
The value of y = KX + B is greater than the function value of y = - 2x + 2
kx+b>-2x+2
(k+2)x>2-b
k> - 2, x > (2-B) / (K + 2)
k
[urgent] the function f (x) = x ^ 2 + 2x + 3 is known. When x ∈ [- 2,2], f (x) = f (x) - KX is a monotonic function. Find the value range of real number K
k> 6 or K < - 2, which can be obtained by classified discussion
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