On the interval left( 0, frac{pi}{2} right),t | vedclass

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

Question

(A) Let $f(x) = \log(\sin x)$.To determine if the function is increasing or decreasing,we find its derivative $f'(x)$.$f'(x) = \frac{d}{dx}(\log(\sin

Vedclass · Accepted Answer

Increasing

Vedclass · Answer

(A) Let $f(x) = \log(\sin x)$.To determine if the function is increasing or decreasing,we find its derivative $f'(x)$.$f'(x) = \frac{d}{dx}(\log(\sin x)) = \frac{1}{\sin x} \cdot \cos x = \cot x$.In the interval $\left( 0, \frac{\pi}{2} \right)$,the value of $\cot x$ is always positive (since both $\sin x$ and $\cos x$ are positive in the first quadrant).Since $f'(x) > 0$ for all $x \in \left( 0, \frac{\pi}{2} \right)$,the function $f(x) = \log(\sin x)$ is strictly increasing on this interval.Therefore,the correct option is $A$.

On the interval $\left( 0, \frac{\pi}{2} \right)$,the function $\log(\sin x)$ is

Similar Questions

Let $f$ be a function defined on $[a, b]$ such that $f^{\prime}(x) > 0$ for all $x \in (a, b)$. Prove that $f$ is an increasing function on $(a, b)$.

In which interval is the function $f(x) = \tan^{-1}(\sin x + \cos x)$ an increasing function?

If $f(x)=\sqrt{3} \sin x-\cos x-2 a x+b$ decreases for all values of $x$,then

Find the intervals in which the function $f$ given by $f(x) = \sin x + \cos x$,$0 \leq x \leq 2 \pi$ is increasing or decreasing.

Let $f(x) = \int \frac{x^2-3x+2}{x^4+1} \, dx$. Then the function decreases in the interval:

Vedclass Test Series

Exam Paper Generator

Online Exam Module