Determine the stationary points of y=(5x^2)/(lnx)

Differentiate y with respect to x using quotient rule:y'=[(1/x)(5x^2)-(10x)(lnx)]/(lnx)^2 =[5x-10xlnx]/(lnx)^2Stationary points occur when y'=0, so when y'=0 we have:5x-10xlnx = 0x(5-10lnx)=0So x=0 or 5-10lnx=0But when x=0, lnx is undefined, so there is no y value at x=0. So x cannot equal 0.Therefore: 5-10lnx=0 x=e^0.5Substitute back into y, we obtain:y=5e/0.5 = 10eSo Sationary Point is: (e^0.5, 10e)

JL
Answered by Jimmy L. Maths tutor

3553 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve 29cosh x – 3cosh 2x = 38 for x, giving answers in terms of natural logarithms


Differentiate: (12x^3)+ 4x + 7


Differentiate y = 4ln(x)x^2


Differentiate 3x^2 + 4x - 7


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences