The function f(x) = x + cos x is | vedclass

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

Question

(A) Given the function $f(x) = x + \cos x$. To determine the nature of the function,we find its derivative with respect to $x$: $f'(x) = \frac{d}{dx}(

Vedclass · Accepted Answer

Always increasing

Vedclass · Answer

(A) Given the function $f(x) = x + \cos x$. To determine the nature of the function,we find its derivative with respect to $x$: $f'(x) = \frac{d}{dx}(x + \cos x) = 1 - \sin x$. We know that for any real number $x$,the range of $\sin x$ is $[-1, 1]$. Therefore,$1 - \sin x \ge 0$ for all $x \in \mathbb{R}$. Specifically,$f'(x) = 0$ only at points where $\sin x = 1$ (i.e.,$x = 2n\pi + \frac{\pi}{2}$),and $f'(x) > 0$ elsewhere. Since $f'(x) \ge 0$ for all $x$ and does not vanish on any interval,the function $f(x)$ is strictly increasing on $\mathbb{R}$.

The function $f(x) = x + \cos x$ is

Similar Questions

The function $f(x) = \frac{x}{x^2-6x-16}$,where $x \in \mathbb{R} - \{-2, 8\}$,

Let $f(x) = x^3 + bx^2 + cx + d$ where $0 < b^2 < c$. Then $f(x)$:

In which of the following intervals does $f(x) = 2x^3$ increase less rapidly than $g(x) = 9x^2 - 12x + 6$?

In which interval is the given function $f(x) = 2x^3 - 15x^2 + 36x + 1$ monotonically decreasing?

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?

Vedclass Test Series

Exam Paper Generator

Online Exam Module