Question

The value of c in Lagrange's theorem for the function

f(x) = log sin x in the interval $\left\lbrack \frac{\pi}{6},\frac{5\pi}{6} \right\rbrack$ is

• A. $\frac{\pi}{4}$
• B. $\frac{\pi}{2}$
• C. $\frac{2\pi}{3}$
• D. None of these

Answer 1

Answer: (B)

$\frac{\pi}{2}$

Answer 2

f(x) = log sin x ® continuous & differentiable

f(p/6) = log sin (p/6) = log(1/2)

f(5p/6) = log sin(5p/6) = log(1/2)

f ¢(x) = cotx

now

f ¢(x) = $\frac{f(5\pi/6)–f(\pi/6)}{5\pi/6–\pi/6}$

̃ cot x = 0

̃ x = p/2 Î (p/6,5p/6)