If f(x) = sin x - cos x, the function is decr | vedclass

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

Question

(D) Given $f(x) = \sin x - \cos x.$First,find the derivative $f'(x)$:$f'(x) = \cos x + \sin x = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos x + \frac{1}{\

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) Given $f(x) = \sin x - \cos x.$First,find the derivative $f'(x)$:$f'(x) = \cos x + \sin x = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos x + \frac{1}{\sqrt{2}} \sin x ight) = \sqrt{2} \sin(x + \pi/4).$For the function to be decreasing,we require $f'(x) $\sqrt{2} \sin(x + \pi/4) $\sin(x + \pi/4) In the interval $0 \le x \le 2\pi$,the argument $	heta = x + \pi/4$ ranges from $\pi/4$ to $9\pi/4$.The sine function is negative in the interval $(\pi, 2\pi)$.Therefore,$\pi Subtracting $\pi/4$ from all sides:$3\pi/4 Comparing this with the given options,none of the intervals provided are subsets of $(3\pi/4, 7\pi/4)$.Thus,the correct option is $(d)$.

If $f(x) = \sin x - \cos x,$ the function is decreasing in the interval $0 \le x \le 2\pi$ for which of the following?

Similar Questions

What type of function is $f(x) = \frac{x - 2}{x + 1}$,where $x \neq -1$?

Function $f(x) = \frac{\lambda \sin x + 3 \cos x}{2 \sin x + 6 \cos x}$ is monotonic increasing,then :

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

The value of $k$ such that the function $f(x) = \sin x - \cos x - kx + b$ is strictly decreasing for all real $x$ is

Which of the following functions is decreasing in the interval $\left(0, \frac{\pi}{8}\right)$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module