GATE 2014 EC (EC3) – Question 11
For $x>-1$, find the x maximizing $f(x)=\ln(1+x)-x$.
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Show answer and explanation
Correct answer: -0.01 to 0.01
Explanation
Differentiate:f′=1/(1+x)−1=−x/(1+x). The denominator is positive on the domain, so the derivative is positive for x<0 and negative for x>0. Thus the global maximum occurs at **x=0**, where f=0.