JEE Main 2020MathematicsApplication of DerivativesEasyMCQ

JEE Main 2020 — Application of Derivatives Question with Solution

JEE Main 2020 (02 Sep Shift 2)

Question

Let f:-1,∞→R be defined by f0=1 and fx=1xloge1+x, x≠0. Then the function f

Choose an option

Show full solutionCorrect option: D
Correct answer
DDecreases in -1,∞

Step-by-step explanation

fx=1xloge1+x, x≠0

f'x=x1+x-ln1+xx2=x-1+xln1+xx21+x

Let gx=x-1+xln1+x

g'x=-ln1+x

⇒g'x>0∀x∈-1,0<0∀x∈0,∞

gmax at x=0⇒g0=0 is the maximum value

So, gx<0∀x∈-1,∞  ⇒ f'x<0∀x∈-1,∞

Hence, fx is decreasing ∀x∈-1,∞

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About this question

This is a previous-year question from JEE Main 2020, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.