It is known that f (x) = ln (AX + 1) + x ^ 3-x ^ 2-ax If f (x) is an increasing function on [1, positive infinity], find the value range of real number a

It is known that f (x) = ln (AX + 1) + x ^ 3-x ^ 2-ax If f (x) is an increasing function on [1, positive infinity], find the value range of real number a

When f (x) = ln (AX + 1) + x ^ 3-x ^ 2-axa = 0, f (x) = x ^ 3-x ^ 2, f '(x) = 3x ^ 2-2x = x (3x-2), [1, positive infinity] on f' (x) > 0, f (x) is an increasing function, so when a = 0, the meaning a ≠ 0, [1, positive infinity) should be in the definition field, when ax + 1 > 0A > 0, x > - 1 / A, - 1 / a ≤ 1, a ≥ - 1a0, obviously g (x) on [1, positive infinity]

Given function f (x) = ln (AX ^ 2 + X-B)
(1) When a = 1, if the domain of function definition is r, find the value range of real number B
(2) When B = - 1, let g (x) = f (2 ^ x) - f (A / 2). If x ∈ (- ∞, 1], G (x) is meaningful, find the value range of real number a

1) If a = 1, f (x) = ln (x ^ 2 + X-B) is defined as R, then x ^ 2 + X-B > 0 is constant on R, then △ 0, a ^ 3 + 2A + 4 > 0, let H (a) = a ^ 3 + 2A + 4, H '(a) = 3A ^ 2 + 2 > 0, so h (a) increases monotonically, H (- 3 / 4) = - 27 / 64-3 / 2 + 4 > 0, so when a > - 3 / 4, H (a) > 0 is synthesized: a > - 3 / 4

Find LIM (x → 0) f (x) / X given f (x) = ln (1 + x)

lim(x→0) f(x)/x
=f'(0)
=1