Applications Of Derivatives Question 252
Question: Consider the following statements S and R S : Both $ \sin x $ and cosx are decreasing functions in $ ( \frac{\pi }{2},\pi ) $ R : If a differentiable function decreases in (a, b) then its derivative also decreases in (a, b). Which of the following is true
[IIT Screening 2000]
Options:
A) Both S and R are wrong
B) Both S and R are correct but R is not the correct explanation for S
C) S is correct and R is the correct explanation for S
D) S is correct and R is wrong
Show Answer
Answer:
Correct Answer: D
Solution:
From the trend of value of $ \sin x $ and $ \cos x $ we know $ \sin x $ and $ \cos x $ decrease in $ \frac{\pi }{2}<x<\pi $ . So, the statement S is correct.
The statement R is incorrect which is clear from graph. Clearly $ f(x) $ is differentiable in (a, b).
Also, $ a<x_1<x_2<b $ . But $ {f}’(x_1)=\tan {\varphi_1}<\tan {\varphi_2}={f}’(x_2). $
BETA
