Given the function f (x) = x ^ 3 + ax * x-x + 2, if f (x) is a decreasing function on (0,1), then the maximum value of A

Given the function f (x) = x ^ 3 + ax * x-x + 2, if f (x) is a decreasing function on (0,1), then the maximum value of A

F (x) '= 3x & # 178; + 2ax-1 (3x & # 178; - 1) / 2x, X ∈ (0,1), X is less than 1, so it is less than the value when x is 1, that is, a = 1

The maximum value of the function y = x + ax + 3 (0 < a < 2) on [- 1,1] is () the minimum value () ask for the help of the great God
Why is the maximum value taken at x = 1 and its value is 4 + A, and why is the minimum value taken at x = - A2 and its value is. I know that the opening of symmetry axis ∈ (- 1,0) image is upward, which is why the previous two can't figure it out. Please help me. Thank you

If the opening is upward, if the axis of symmetry can be taken as 0, then there are two maximum values, x = - 1. X = 1. But if it can't be taken, it can move to the left, so the maximum value is x = 1. If the minimum value is the axis of symmetry, the axis of symmetry is x = - B / 2A = - A / 2

Given that the function f (x) = - X3 + ax is a decreasing function on [1, + ∞), then the maximum value of a is

The derivative of the function is f '(x) = - 3x ^ 2 + A. so a

High school mathematics function problem known function f (x) = x ^ 3 - x ^ 2 + ax + B
Let f (x) = x ^ 3-x ^ 2 + ax + B. let any x1, X2 ∈ (0,1), and x1 ≠ x2 have f (x1) - f (x2)

Let any x1, X2 ∈ (0,1), and x1 ≠ X2, have f (x1) - f (x2)