Statement 1: The function `f(x)=x` In `x` is increasing in `(1/e ,oo)` Statement 2: If both `f(x)a n dg(x)` are increasing in `(a , b),t h e nf(x)g(x)` must be increasing in (a,b).

Statement 1: The function f(x)=x In x is increasing in ((1)/(e),oo) Statement 2: If both f(x) and g(x) are increasing in (a,b), then f(x)g(x) must be increasing in (a,b).

f(x) = x^(2) e^(-x) is increasing in

Prove that the function f(x)=(log)_e x is increasing on (0,\ oo) .

Prove that the function f(x)=log_(e)x is increasing on (0,oo)

Prove that the function f(x)=(log)_(e)x is increasing on (0,oo)

f(x)=(x+2)e^(-x) is increasing in ………….

The function f(x) = x^(2) e^(-x) strictly increases on

Statement 1: The function x^(2)(e^(x)+e^(-x)) is increasing for all x>0 statement 2: The functions x^(2)e^(x) and x^(2)e^(-x) are increasing for all x>0 and the sum of two infunctions in any interval (a,b) is an increasing function in (a,b).