Because the function f(x) is monotonically increasing in the interval (0, 1), f' (x) represents the slope, and the slope of any point of f '(x) is positive in (0, 1), so f' (x) = () e x >: 0 because e is about.
So a+ax-1>; =0 combine 0 and 1 into one> =1/2a > = 1 {comprehensive a>= 1
Explain the exponential function: y = a x a >；; In 1 (equivalent to E in this question), the image is increased by 0; =0
"2" (1) still calculates the derivative of f(x), and then substitutes x= 1 to get f' (x) =1-2x+b/x. Since the slope is 2, f' (1) = 2 is obtained.
(2) So f(x) = x = x 2+3lnx If f (x) is less than or equal to 2x-2, then f(x)-2x+2 is less than or equal to 0, that is, if f (x)-2x+2 =-x 2-x+3lnx+2 is less than or equal to 0. Just prove that f (. Then G'(x)=-2x- 1+3/x, because it is over (1, 0), so G'(x)=0 gets x=- 1.5 or 1 because the domain of x is a positive real number.
Therefore, if x=- 1.5 is discarded, that is, G( 1) is the maximum value, and G( 1)=0, that is, G(x)≤0, that is, F (X) ≤ 2x-2.
I calculate word for word, and I hope the subject will give points.