Question

determne the values of X for which f (x)=x^x, x> 0 is increasing or decreaseing​

Answer 1

Step-by-step explanation:

Answer

f(x)=x

x

The interval in which f(x) is increasing is one in which f

′

(x)>0.

Now,

f

′

(x)=x

x

ln(x)+x

x

=x

x

(ln x+1)

For f

′

(x)>0,

ln x+1>0

ln x>−1

x>

e

1

Thus, the function x

x

is increasing in the interval (

e

1

,∞).