A) decreasing function
B) increasing function
C) not monotonic
D) None of the above
Correct Answer: A
Solution :
\[f(x)=\frac{x}{1+x}-\log (1+x),x>0\] \[f'(x)=\frac{(1+x).1-x.1}{{{(1+x)}^{2}}}-\frac{1}{1+x}\] \[=\frac{1}{{{(1+x)}^{2}}}-\frac{1}{1+x}\] \[=\frac{1-(1+x)}{{{(1+x)}^{2}}}=-\frac{x}{{{(1+x)}^{2}}}\] If\[x>0,\]then\[f'(x)\]decreases \[\therefore \] \[f(x)\]is decreasing function.
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