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The function x^x decreases in the interv...

The function `x^x` decreases in the interval `(0,e)` (b) `(0,1)` `(0,1/e)` (d) none of these

A

(0,e)

B

(0,1)

C

`(0,(1)/(e ))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
3
`f(x) = x^(x)[1+logx]=x^(x) log (ex)`
`f(x)lt0`
or `log(ex)lt0`
or `0ltexlt1`
or `0ltexxle1//e`
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CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Single)
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  16. Let f: RvecR be a differentiable function for all values of x and has ...

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  17. Let f: Rvec be a differentiable function AAx in R . If the tangent dr...

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  18. Let f(x) be a function such that f(x)=(log)(1/2)[(log)3(sinx+a]dot If...

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  19. If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x...

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