In which of the following intervals does f(x) | vedclass

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

Question

(A) To determine where $f(x) = \sin x$ increases less rapidly than $g(x) = \cos x$,we compare their derivatives.$f'(x) = \cos x$ and $g'(x) = -\sin x$

Vedclass · Accepted Answer

$\left( -\frac{\pi}{2}, -\frac{\pi}{4} \right)$

Vedclass · Answer

(A) To determine where $f(x) = \sin x$ increases less rapidly than $g(x) = \cos x$,we compare their derivatives.$f'(x) = \cos x$ and $g'(x) = -\sin x$.We want to find the interval where $f'(x) This is equivalent to $\sin x + \cos x Dividing by $\sqrt{2}$,we get $\frac{1}{\sqrt{2}} \sin x + \frac{1}{\sqrt{2}} \cos x This inequality holds when $\pi Solving for $x$,we get $-\frac{5\pi}{4} Among the given options,the interval $\left( -\frac{\pi}{2}, -\frac{\pi}{4} \right)$ is a subset of this range.Therefore,in the interval $\left( -\frac{\pi}{2}, -\frac{\pi}{4} \right)$,$f(x)$ increases less rapidly than $g(x)$.

In which of the following intervals does $f(x) = \sin x$ increase less rapidly than $g(x) = \cos x$?

Similar Questions

The range of values of $x$ for which $f(x)=x^3+6x^2-36x+7$ is increasing is:

Let $f(x) = e^x - e^{-x} + \cos x$,then $f(x)$ is

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.

If $f(x)=x^3+a x^2+b x+5 \sin ^2 x$ is an increasing function on $R$,then

The function $f(x) = \sin^4 x + \cos^4 x$ increases,if

Vedclass Test Series

Exam Paper Generator

Online Exam Module