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  • Explain solution rd Sharma class 12 chapter 16 Increasing and decreasing function exercise multiple choice question, question 35

Explain solution rd sharma class 12 chapter 16 Increasing and decreasing function exercise multiple choice question, question 35

Answers (1)

Always increases (Option a)

Hints: Find the derivative of functions

Given: f(x)=\tan x-x

Solution:

We have,              \begin{aligned} &f(x)=\tan x-x \\ &f^{\prime}(x)=\sec ^{2} x-1>0 \end{aligned}

                              Or

                   \begin{aligned} &\sec ^{2} x>1 \end{aligned}

Now

               \begin{aligned} &\cos x \in[-1,1] \\ &\sec x \in(-\infty,-1] \cup[1, \infty) \end{aligned}

Thus,

               \sec ^{2} x \in[1, \infty)

Hence,

               f^{\prime}(x)>0 \forall x

Function f(x)=\tan x-x is always increasing.

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