- Home
- Standard 12
- Mathematics
5. Continuity and Differentiation
easy
यदि $f(x) = \cos x,0 \le x \le \frac{\pi }{2}$, तो मध्यमान प्रमेय की वास्तविक संख्या $ ‘c’$ है
A
$\frac{\pi }{6}$
B
$\frac{\pi }{4}$
C
${\sin ^{ - 1}}\left( {\frac{2}{\pi }} \right)$
D
${\cos ^{ - 1}}\left( {\frac{2}{\pi }} \right)$
Solution
(c) हम जानते हैं कि $f'(c) = \frac{{f(b) – f(a)}}{{b – a}}$
$ \Rightarrow f'(c) = \frac{{0 – 1}}{{\pi /2}} = – \frac{2}{\pi }$…..$(i)$
किन्तु $f'(x) = – \sin x \Rightarrow f'(c) = – \sin c$….$(ii)$
$(i)$ व $(ii)$ से, $ – \sin c = – \frac{2}{\pi } \Rightarrow c = {\sin ^{ – 1}}\left( {\frac{2}{\pi }} \right)$
Standard 12
Mathematics
