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Question 29 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at March 29, 2023 by

f (x) = xx has a stationary point at

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

(C) x = 1                      (D) x = √e

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Question 29 f (x) = xx has a stationary point at (A) x = e (B) x = 1/𝑒 (C) x = 1 (D) x = βˆšπ‘’ A stationary point of a function is a point where 𝒇′(𝒙) = 0 For differentiating f (π‘₯), we use logarithmic differentiation f (π‘₯) = π‘₯^π‘₯ Taking log on both sides log f (𝒙) = 𝒙 log 𝒙 Differentiating w.r.t. x 1/𝑓(π‘₯) 𝑓′(π‘₯) = π‘₯ . 1/π‘₯ + 1. log π‘₯ 1/π‘₯^π‘₯ 𝑓′(π‘₯) = 1 + log π‘₯ 𝒇′(𝒙) = 𝒙^𝒙(1 + log 𝒙) Putting 𝒇’(x) = 0 π‘₯^π‘₯ ("1 + log " π‘₯" " )=𝟎 Either 𝒙^𝒙 = 0 Since, π‘₯^π‘₯ is exponential function it can never be zero. Or 1 + log 𝒙 = 0 log π‘₯ = βˆ’1 Taking exponential on both sides 𝒆^π’π’π’ˆβ‘π’™ = 𝒆^(βˆ’πŸ) π‘₯ = 𝑒^(βˆ’1) 𝒙 = 𝟏/𝒆 Hence, Stationary point is 𝒙 = 𝟏/𝒆 So, the correct answer is (B)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.