InterviewSolution
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InterviewSolution
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The fraction exceeds its `p^(th) ` power by the greatest number possible, where `p geq2` isA. `((1)/(p))^(1//(p-1))`B. `((1)/(p))^(p-1)`C. `p^(1//p-1)`D. none of these |
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Answer» Correct Answer - A Let `y=x-x^(p)`, where x is the fraction `rArr" "(dy)/(dx)=1-px^(p-1)` For maximum of minimum, `(dy)/(dx)=0` `rArr" "1-px^(p-1)=0 rArrx=((1)/(p))^(1//(p-1))` Now, `(d^(2)y)/(dx^(2))=-p(p-1)x^(p-2)` `therefore(d^(2)y)/(dx^(2)):|_(x=((1)/(p))^(1//(p-1)))=-p((1)/(p))^((p-2)//(p-1))lt0` `therefore "y is maximum at x"=((1)/(p))^(1//(p-1))` |
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