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Please solve RD Sharma class 12 chapter 16 Increasing and Decreasing Function Excercise Very Short Answer type Question 13 Maths Textbook Solution.

Answers (1)

Answer:

The function f(x)  is increasing in its domain.

Hint:

f(x)  is increasing, if  f'(x)>0

f(x)  is decreasing, if  f'(x)<0

Given:

                f(x)=\tan x-x

Explanation:

It is given that,

                f(x)=\tan x-x                                                                                                                                            

Differentiate equation (i) with respect to x

\Rightarrow         f'(x)=\sec ^{2}x-1

\because           \sec ^{2}x-1>0  for all  x

\therefore           f(x) is an increasing function.

Thus, the given function is increasing in its domain.

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