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The fraction exceeding its pth power by ...

The fraction exceeding its pth power by the greatest number possible, where `p ge 2`, is

A

`(1/n)^(1/(n-1))`

B

`(1/n)^(n-1)`

C

`n^(1/n-1)`

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let x be the fraction and let `y=x-x^n` . Then
`dy/dx=1-nx^(n-1)and (d^(2)y)/(dx^2)=-n(n-1)x^(n-2)`
Now `,(dy)/(dx) =0 rarr x= (1/n)^(1/(n-1))`
Clearly `(d^2y)/(dx^2) lt 0 " for " x =(1/n)^(1/(n-1))`
Hence , y is maximum when `x=(1/n)^(n-1)`
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