f (x) = xx has a stationary point at
(A) x = e (B) x = 1/e
(C) x = 1 (D) x = √e
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Question 16 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives
Last updated at July 21, 2026 by Teachoo
NCERT Exemplar - MCQs
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Chapter 6 Class 12 Application of Derivatives
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Question 16 f (x) = xx has a stationary point at (A) x = e (B) x = 1/š (C) x = 1 (D) x = āš A stationary point of a function is a point where šā²(š) = 0 For differentiating f (š„), we use logarithmic differentiation f (š„) = š„^š„ Taking log on both sides log f (š) = š log š Differentiating w.r.t. x 1/š(š„) šā²(š„) = š„ . 1/š„ + 1. log š„ 1/š„^š„ šā²(š„) = 1 + log š„ šā²(š) = š^š(1 + log š) Putting šā(x) = 0 š„^š„ ("1 + log " š„" " )=š Either š^š = 0 Since, š„^š„ is exponential function it can never be zero. Or 1 + log š = 0 log š„ = ā1 Taking exponential on both sides š^šššā”š = š^(āš) š„ = š^(ā1) š = š/š Hence, Stationary point is š = š/š So, the correct answer is (B)
