Given the function f (x) = − 14x4 + 23x3 + AX2 − 2x − 2, it decreases monotonically in the interval [- 1,1] and increases monotonically in the interval [1,2]. Find the value of real number a

Given the function f (x) = − 14x4 + 23x3 + AX2 − 2x − 2, it decreases monotonically in the interval [- 1,1] and increases monotonically in the interval [1,2]. Find the value of real number a

∵ the function f (x) = − 14x4 + 23x3 + AX2 − 2x − 2 decreases monotonically in the interval [- 1,1], increases monotonically in the interval [1,2] ∵ when x = 1 gets the minimum, ∵ f ′ (1) = 0 ∵ f ′ (1) = - X3 + 2x2 + 2ax-2 ∵ f ′ (1) = - X3 + 2x2 + 2ax-2 = 0, a = 12, so the value of real number a is 12

If the function f (x) = x & # 179; - ax increases monotonically in the interval [1, + ∞), then the maximum value of a is?

f'(x)=3x²-a
F (x) increases monotonically in the interval [1, + ∞];
That is, f '(x) ≥ 0 is [1, + ∞) constant for X;
3x²-a≧0
Then a ≤ 3x & # 178;
Then a should be less than or equal to the minimum value of 3x & #,
Because x belongs to [1, + ∞), the minimum value of 3x & # is 3;
So: a ≤ 3
The maximum value of a is 3;

Given that a > 0, f (x) = X3 ax is a monotone increasing function on [1, + ∞), then the maximum value of a is ()
A. 0B. 1C. 2D. 3

From the meaning of the problem, we get that f ′ (x) = 3x2-a, ∵ function f (x) = X3 ax is a monotone increasing function on [1, + ∞), f ′ (x) ≥ 0 holds constant on [1, + ∞), that is, a ≤ 3x2 holds constant on [1, + ∞), and a ≤ 3