If `xgt0` then the minimum value of `x^x` is

If xgt 0 the minimum value of x^x is

Let exp(x) denote exponential function e^x . If f(x)=exp(x^(1/x)).xgt0 then the minimum value of f in the interval [2,5] is

Statement-I : f(x)=sqrt3sinx+cosx has a greatest value when x=pi/6 Statement-II : If xgt0,xy=1 the minimum value of x + y is 2 Which of the above statements is true

x and y be two variables such that xgt0 and xy=1 . Then the minimum value of x+y is

The maximum value of (1/x)^x, xgt0 is

If xgt0,ygt0,x+y=3 and xy is maximum then the maximum value of xy is

If xgt0,ygt0 and x+y=1, then find the minimum value of x log x + y log y.

If the median of (x)/(5),x,(x)/(4),(x)/(2),(x)/(3)(xgt0) is 8, then the value of x is

xgt0,ygt0 and x+y=1 . The minimum value of xlogx+ylogy is