If the function y = (log12a) x is an increasing function on R, then the value range of a is () A. （0，12）B. (0，12]C. (12，+∞)D. （1，+∞）

If the function y = (log12a) x is an increasing function on R, then the value range of a is () A. （0，12）B. (0，12]C. (12，+∞)D. （1，+∞）

∵ y = (log12a) x is an increasing function on R, so a is chosen

Given the function f (x) = X3 + AX2 + B, the tangent of the image at point P (1,0) is parallel to the line 3x + y = 0
(1) Find the value of constant a and B;
(2) Find the minimum and maximum of function f (x) in the interval [0, t]. (T > 0)
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A:
(1).
F (x) is defined as X ∈ R
F '(x) = 3x & # 178; + 2aX, f' (1) = 3 + 2A = - 3, so a = - 3
F (1) = 1-3 + B = 0, so B = 2
So a = - 3, B = 2
(2)
f(x)=x³-3x²+2,f'(x)=3x²-6x
When f '(x) = 0, 3x & # 178; - 6x = 0, that is, X (X-2) = 0, the solution is X1 = 0, X2 = 2
x ∈ (-∞,0) ,0 ,(0,2) ,2 ,(2,+∞)
f'(x) >0 ,=0 ,0
F (x) is increasing, maximum, decreasing, minimum, increasing
Because t > 0, so:
① When 0

Given the function f (x) = ax ^ 2 + 1 (a > 0) g (x) = x ^ 3 + BX, when a ^ 2 = 4b, find the monotone interval of the function f (x) + G (x), and find the monotone interval of the function f (x) + G (x)
The maximum of (- ∞, - 1]

Let H (x) = f (x) + G (x) = x ^ 3 + ax ^ 2 + BX + 1 get: H '(x) = 3x ^ 2 + 2aX + B from a > 0 and a ^ 2 = 4B know: H' (x) = 3x ^ 2 + 2aX + B = H '(x) = 3x ^ 2 + 2aX + A ^ 2 / 4 = (3x + A / 2) (x + A / 2) H' (x) = 0 get x = - A / 2, x = - A / 6, so the monotone increasing interval of H (x) = f (x) + G (x) is (- ∞, - A / 2] ∪ [- A / 6, + ∞

It is proved that the function f (x) = 2x − 5x2 & nbsp; + 1 has at least one zero point in the interval (2,3)

It is proved that: ∵ f (x) = 2x − 5x2 & nbsp; + 1 is a continuous function on the interval (2,3) and ∵ f (2) = − 15 < 0, f (3) = 110 > 0. From the judgment theorem of zero point of function, we can know that f (x) has at least one zero point on (2,3)