Let f (x) = LNX, G (x) = f (x) + F '(x) 1) Finding the monotone interval and minimum of G (x) 2) Discuss the size of G (x) and G (1 / x) 3) Find the value range of a so that G (a) - G (x) 0 holds

Let f (x) = LNX, G (x) = f (x) + F '(x) 1) Finding the monotone interval and minimum of G (x) 2) Discuss the size of G (x) and G (1 / x) 3) Find the value range of a so that G (a) - G (x) 0 holds

1)f'(x)=1/x
g(x)=lnx+1/x
g'(x)=1/x-1/x^2=(x-1)/x^2=0,x=1
X0, monotone increasing interval
When the minimum value is x = 1, G (1) = 1
2)g(1/x)=-lnx+x
y=g(x)-g(1/x)=2lnx+1/x-x
y'=2/x-1/x^2-1=(2x-1-x^2)/x^2=-(x-1)^2/x^2

Elden Ring Premiere

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