Application of Derivatives 2 Question 25

25. Match the conditions/expressions in Column I with statements in Column II.

Let the functions defined in Column I have domain $(-\pi / 2, \pi / 2)$.

Column I
A. $x+\sin x$ p. increasing
B. $\sec x$ q. decreasing
r. neither increasing nor decreasing

Analytical & Descriptive Questions

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Answer:

Correct Answer: 25. (c)

Solution:

  1. $\frac{d}{d x}(x+\sin x)=1+\cos x=2 \cos ^{2} \frac{x}{2}>0$ for $-\frac{\pi}{2}<x<\frac{\pi}{2}$.

Therefore, $x+\sin x$ is increasing in the given interval. Therefore, $(A) \rightarrow(p)$ is the answer.

Again, $\frac{d}{d x}(\sec x)=\sec x \tan x$ which is $>0$ for $0<x<\pi / 2$ and

$$ <0 \text { for } \frac{-\pi}{2}<x<0 $$

Therefore, sec $x$ is neither increasing nor decreasing in the given interval. Therefore, $(B) \rightarrow(r)$ is the answer.



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