Q. 23

Which fraction exceeds its pth power by the greatest number possible?

Answer :

Given,


The pth power of a number exceeds by a fraction to be the greatest.


Let us consider,


‘x’ be the required fraction.


The greatest number will be y = x - xp ------ (1)


For finding the maximum/ minimum of given function, we can find it by differentiating it with x and then equating it to zero. This is because if the function y(x)has a maximum/minimum at a point c then y’(c) = 0.


Differentiating the equation (1) with respect to x:



---- (2)


[Since ]


To find the critical point, we need to equate equation (2) to zero.



1 = pxp-1



Now to check if this critical point will determine the if the number is the greatest, we need to check with second differential which needs to be negative.


Consider differentiating the equation (2) with x:



----- (3)


[Since ]


Now let us find the value of



As , so the number y is greatest at


Hence, the y is the greatest number and exceeds by a fraction


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
How to find Maxima & Minima?How to find Maxima & Minima?How to find Maxima & Minima?43 mins
Practise Questions - Application of DerivativesPractise Questions - Application of DerivativesPractise Questions - Application of Derivatives45 mins
Interactive quizz on tangent and normal, maxima and minimaInteractive quizz on tangent and normal, maxima and minimaInteractive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minimaInteractive quiz on maxima and minimaInteractive quiz on maxima and minima48 mins
Tangent & Normal To A CurveTangent & Normal To A CurveTangent & Normal To A Curve53 mins
Test your knowledge of Tangents & Normals (Quiz)Test your knowledge of Tangents & Normals (Quiz)Test your knowledge of Tangents & Normals (Quiz)52 mins
Tangents & Normals (Concept Builder Class)Tangents & Normals (Concept Builder Class)Tangents & Normals (Concept Builder Class)55 mins
Few Applications of Gauss's lawFew Applications of Gauss's lawFew Applications of Gauss's law54 mins
Application of Biotechnology | Concepts - 02Application of Biotechnology | Concepts - 02Application of Biotechnology | Concepts - 0256 mins
Applications of Ampere's Circuital LawApplications of Ampere's Circuital LawApplications of Ampere's Circuital Law44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :