discuss the monotonicity of the function x raise to power x ,(x>0)

Asked by imanumaan | 23rd Nov, 2009, 04:53: PM

Expert Answer:

Let y =x  x

Taking log  we have

log y = x log x

dy/dx = y(1+log x)  =x(1+log x)  which is greater than 0 for all values of  x>0

so x  x    is   monotonically increasing function

Answered by  | 24th Nov, 2009, 09:55: AM

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