" 3.Show that "x+(1)/(x)" is increasing on "(1,oo)

Show that x^(1//x) is increasing in (0,e) and decreasing in (e,oo) . Hence determine which of e^pi,pi^e is greater.

Show that f(x)=(1)/(x) is a decreasing function on (0,oo)

Show that f(x)=(1)/(x) is decreasing function on (0,oo)

Show that f(x)=1/x is decreasing function on (0,oo)dot

Show that f(x)=|x| is strictly decreasing on (-oo, 0) and strictly increasing on (0, oo) .

Obsereve the following the lists {:("List-I","List-II"),("A) "f(x)=x^2-2x+5" is increasing in","1) "xgt1/e),("B) "f(x)=x^x" decreases for","2) "(-oo,-1)uu(1,oo)),("C) "f(x)=x+1/x" is increasing in","3) "(1,oo)),("D) "f(x)=9-6x-2x^2-x^3" is decreasing for","4) "(-oo,oo)),("","5) "0ltxlt1/e):}

Show that f(x)=1/x is a decreasing function on (0,\ oo) .

Let f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1), then: (a) g is increasing on (1,oo) (b) g is decreasing on (1,oo) (c) g is increasing on (1,2) and decreasing on (2,oo) (d) g is decreasing on (1,2) and increasing on (2,oo)

Show that the function x+1/x is increasing for x>1.

1.Prove that the function f(x)=log_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo), if '0