Let p be a point on the curve C: y = - 1 / 3x & # 179; + X & # 178; - 2x + A, and the inclination angle a of the tangent line of curve C at point P, then the value range of a is obtained (2) given the function f (x) = ㏑ x, G (x) = ax & # 178; / 2 + 2x (a ≠ 0), if f ′ (x) > G ′ is constant on (0, + ∞), the value range of a is obtained

Let p be a point on the curve C: y = - 1 / 3x & # 179; + X & # 178; - 2x + A, and the inclination angle a of the tangent line of curve C at point P, then the value range of a is obtained (2) given the function f (x) = ㏑ x, G (x) = ax & # 178; / 2 + 2x (a ≠ 0), if f ′ (x) > G ′ is constant on (0, + ∞), the value range of a is obtained

1、
y'=x²+2x-2=(x+1)²-3≧-3
That is: k = Tana ≥ - 3
A ∈ [0, π / 2] u [π + arctan (- 3), π]
2、
f'(x)=1/x,g'(x)=ax+2
1/x>ax+2
Namely: ax0
So, A0, then: 1 / x > 0, so when 1 / x = 1, H (x) has a minimum value of - 1
Therefore, H (x) ≥ - 1
a

Let a be a real number, Let f (x) = ax LNX, and let the tangent of the curve y = f (x) at point P (1, f (1)) be parallel to the straight line 2x + 3y-3 = 0
Let a be a real number, Let f (x) = ax LNX, and let the tangent of the curve y = f (x) at point P (1, f (1)) be parallel to the straight line 2x + 3y-3 = 0. (1) find the analytic expression of the function y = f (x) (2) find the minimum of the function y = f (x)

1.f'(x)=a-1/x
F '(1) = A-1 = - 2 / 3
a=1/3
f(x)=x/3-lnx
2.f'(x)=1/3-1/x
Let f '(x) = 0, then: x = 3
Ψ f (x) decreases monotonically on (- ∞, 3) and increases monotonically on (3, + ∞)
The minimum value of F (x) is: F (3) = 1-ln3