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Given the function f (x) = alnx - (1 + a) x + 0.5x ^ 2, (a belongs to R), if f (x) > = 0, it holds for any X in the domain of definition, and the value range of a is obtained
F (x) = alnx - (1 + a) x + 0.5x ^ 2 > = 0 holds on x > 0
A (lnx-x) > = x-0.5x * x is obtained
And lnx-x0 (x = 2)
When x
If the definition field of function = 1 / LG (X & # 178; + BX + 2b) is r, then the value range of B is?
Given that the function f (x) = x2 + 2 (A-1) x + 2 is an increasing function on [4, + ∞), then the value range of real number a is______ ．
∵ f (x) = x2 + 2 (A-1) x + 2 is an increasing function on [4, + ∞], and the symmetry axis 1-A ≤ 4 is a ≥ - 3, so the answer is: [- 3, + ∞)
Given that the function y = x ^ 2 - 2x + 3 has a maximum value of 3 and a minimum value of 2 in the closed interval [0, M], what is the range of M?
The answer is [1.2], why not (0.2), and why can't I choose between 0 and 1
First, y = x & # 178; - 2x + 3 is sorted into y = (x-1) &# 178; + 2,
We can see that y = (x-1) ² + 2, when x is a real number, its minimum value is 2, and its maximum value is infinite,
Because y = (x-1) &# 178; + 2, its symmetry axis is x = 1, and the minimum value is obtained if and only if x = 1
When x = 0 or x = 2, the value of the function is 3,
So when x is in the interval [0,2], the minimum value of function y is 2 and the maximum value is 3
So the value of M is [1.2]
(if M
RELATED INFORMATIONS
- 1. The known function f (x) = x ^ 2 + alnx
- 2. Given the function f (x) = 2 / x + alnx, a ∈ R (1) If a = 4, find the monotone interval of function f (x) (2) If the function f (x) increases monotonically on [1, + 00], find the value range of real number a
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- 4. Given the function f (x) = x2 + (2a-1) x-alnx, G (x) = - 4 / x-alnx, (a ∈ R) The function f (x) = x2 + (2a-1) x-alnx, G (x) = - 4 / x-alnx (a ∈ R) is known (1) When a ＜ 0, find the minimum of F (x); (2) If the image of the function y = f (x) and y = g (x) has two different intersections m, N on X ∈ [1,3], the value range of a is obtained
- 5. The known function f (x) = ((x ^ 2) / 2) - alnx (a)
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