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Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Fill in the blanks Question 4: Maths Textbook Solution.

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Answer: The largest open interval in which the function decreases is (0,\infty )

Hint: if the function f(x) is decreasing then f'(x)<0

Given: f(x)=\frac{1}{1+x^{2}}    ...(i)

Explanation: Differentiate (i) with respect to x


Now, f'(x)=-\frac{2x}{(1+x^{2})^{2}}<0                       [  \because f(x) is decreasing]

\Rightarrow -2x<0

\Rightarrow x>0

\therefore x\epsilon (0,\infty )

Thus, the largest interval is which f(x) decreases is (0,\infty )

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