Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

If the tangent to the curve, y=f(x)=x\; \log_{e}x,(x>0) at a point (c,f(c)) is parallel to the line - segment joining the points (1,0) and (e,e), then c is equal to :
Option: 1 \frac{e-1}{e} 
Option: 2 e^{\left ( \frac{1}{e-1} \right )}
Option: 3 e^{\left ( \frac{1}{1-e} \right )}
Option: 4 \frac{1}{e-1}

Answers (1)

best_answer

\\f(x)=x \log _{e} x \\ \\\left.f^{\prime}(x)\right|_{(c, f(c))}=\frac{e-0}{e-1} \\ \\f^{\prime}(x)=1+\log _{e} x \\ \\\left.f^{\prime}(x)\right|_{(c, f(c))}=1+\log _{e} c=\frac{e}{e-1} \\ \\\log _{c} c=\frac{e-(e-1)}{e-1}=\frac{1}{e-1} \Rightarrow c=e^{\frac{1}{e-1}}

Posted by

himanshu.meshram

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024: NTA debars 39 candidates for 3 years on account of using unfair means
anam-khan

JEE Main 2024 session 2 paper 2 answer key objection window closes today; fees
anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’

Latest Question