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5. Continuity and Differentiation
easy
$\left[ {\frac{\pi }{6},\,\frac{{5\pi }}{6}} \right]\,\,$ અતરલમાં વિધેય ${f}{\text{(x) = logsinx }}$ માટે લાંગ્રાજના પ્રમેયના $c$ નું મૂલ્ય કેટલું થાય $?$
A
$\frac{\pi }{4}$
B
$\frac{\pi }{2}$
C
$\frac{{2\pi }}{3}$
D
એકપણ નહિ
Solution
${f}(x)\,\, = \,\,\log \,\sin \,x$
$L.M.V.T.\,\,$ માટે
$f'{\text{(c)}}\,\, = \,\,\frac{{{f}{\text{(b)}}\,\,{\text{ – }}\,\,{f}{\text{(a)}}}}{{{\text{(b}}\,\,{\text{ – }}\,\,{\text{a)}}}}$
$f'(c)\,\, = \,\,\,\frac{{\log \,\sin \,\frac{{5\pi }}{6}\,\, – \,\,\log \,\sin \frac{\pi }{6}}}{{\frac{{5\pi }}{6}\,\, – \,\,\frac{\pi }{6}}}\,\,\,\,\, = \,\,\frac{{\log \frac{1}{2}\,\, – \,\,\log \frac{1}{2}}}{{\frac{{4\pi }}{6}}}\,\, = \,\,0$
Standard 12
Mathematics
