Applications Of Derivatives Question 385
Question: If $ f(x)=\cos x,0\le x\le \frac{\pi }{2} $ , then the real number -c- of the mean value theorem is
[MP PET 1994]
Options:
A) $ \frac{\pi }{6} $
B) $ \frac{\pi }{4} $
C) $ {{\sin }^{-1}}( \frac{2}{\pi } ) $
D) $ {{\cos }^{-1}}( \frac{2}{\pi } ) $
Show Answer
Answer:
Correct Answer: C
Solution:
We know that $ f’(c)=\frac{f(b)-f(a)}{b-a} $
$ \Rightarrow f’(c)=\frac{0-1}{\pi /2}=-\frac{2}{\pi } $ …..(i) But $ f’(x)=-\sin x\Rightarrow f’(c)=-\sin c $ ….(ii)
From (i) and (ii), we get $ -\sin c=-\frac{2}{\pi }\Rightarrow c={{\sin }^{-1}}( \frac{2}{\pi } ) $ .
BETA
