Question 16 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

f (x) = xx has a stationary point at

(A) x = e (B) x = 1/e

(C) x = 1 (D) x = √e

f (x) = x^x has a stationary point at - Teachoo Class 12 [MCQ] - NCERT Exemplar - MCQs

part 2 - Question 16 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives

part 3 - Question 16 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives

Next: Question 17 Important → Share on WhatsApp

Transcript

Question 16 f (x) = xx has a stationary point at (A) x = e (B) x = 1/𝑒 (C) x = 1 (D) x = √𝑒 A stationary point of a function is a point where 𝒇′(𝒙) = 0 For differentiating f (𝑥), we use logarithmic differentiation f (𝑥) = 𝑥^𝑥 Taking log on both sides log f (𝒙) = 𝒙 log 𝒙 Differentiating w.r.t. x 1/𝑓(𝑥) 𝑓′(𝑥) = 𝑥 . 1/𝑥 + 1. log 𝑥 1/𝑥^𝑥 𝑓′(𝑥) = 1 + log 𝑥 𝒇′(𝒙) = 𝒙^𝒙(1 + log 𝒙) Putting 𝒇’(x) = 0 𝑥^𝑥 ("1 + log " 𝑥" " )=𝟎 Either 𝒙^𝒙 = 0 Since, 𝑥^𝑥 is exponential function it can never be zero. Or 1 + log 𝒙 = 0 log 𝑥 = −1 Taking exponential on both sides 𝒆^𝒍𝒐𝒈⁡𝒙 = 𝒆^(−𝟏) 𝑥 = 𝑒^(−1) 𝒙 = 𝟏/𝒆 Hence, Stationary point is 𝒙 = 𝟏/𝒆 So, the correct answer is (B)

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular