F(x) = log |sin x|,where x in (0, pi),is stri | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given the function $f(x) = \log |\sin x|$ for $x \in (0, \pi)$.Since $x \in (0, \pi)$,$\sin x$ is always positive,so we can write $f(x) = \log(\si

Vedclass · Accepted Answer

$\left(0, \frac{\pi}{2}\right)$ only

Vedclass · Answer

(C) Given the function $f(x) = \log |\sin x|$ for $x \in (0, \pi)$.Since $x \in (0, \pi)$,$\sin x$ is always positive,so we can write $f(x) = \log(\sin x)$.To find the intervals where the function is strictly increasing,we calculate the derivative $f'(x)$:$f'(x) = \frac{1}{\sin x} \cdot \cos x = \cot x$.For the function to be strictly increasing,we must have $f'(x) > 0$.Therefore,$\cot x > 0$.In the interval $(0, \pi)$,$\cot x$ is positive when $x \in \left(0, \frac{\pi}{2}\right)$.Thus,the function is strictly increasing on $\left(0, \frac{\pi}{2}\right)$.

$F(x) = \log |\sin x|$,where $x \in (0, \pi)$,is strictly increasing on

Similar Questions

If $f(x) = \frac{\lambda \sin x + 6 \cos x}{2 \sin x + 3 \cos x}$ is a strictly increasing function,then .......

Find the intervals in which the function given by $f(x) = \frac{3}{10}x^4 - \frac{4}{5}x^3 - 3x^2 + \frac{36}{5}x + 11$ is $(a)$ increasing $(b)$ decreasing.

Show that the function $f$ given by $f(x) = x^{3} - 3x^{2} + 4x$,$x \in R$ is strictly increasing on $R$.

In which interval is the function $f(x) = x^x$ a decreasing function?

The equation $x^3+x-1=0$ has

Vedclass Test Series

Exam Paper Generator

Online Exam Module