Mark the correct alternative in the following: The function f(x) = x x decreases on the interval.

Question

Philoid · Accepted Answer

Formula:- The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on (a,b) is that f’(x)>0 for all x(a,b)

Given:-

f(x) = x^x

now for decreasing

f^’(x)<0

x^x(1+logx)<0

(1+logx)<0

logx<-1

x-1

Mark the correct alternative in the following:The function f(x) = xx decreases on the interval.

Mark the correct alternative in the following:
The function f(x) = x^x decreases on the interval.