If f(x) = kx - sin x is monotonically increas | vedclass

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

Question

(A) function $f(x)$ is monotonically increasing if $f'(x) \geq 0$ for all $x \in R$.Given $f(x) = kx - \sin x$.Differentiating with respect to $x$,we

Vedclass · Accepted Answer

$k > 1$

Vedclass · Answer

(A) function $f(x)$ is monotonically increasing if $f'(x) \geq 0$ for all $x \in R$.Given $f(x) = kx - \sin x$.Differentiating with respect to $x$,we get $f'(x) = k - \cos x$.For $f(x)$ to be monotonically increasing,$f'(x) \geq 0$ for all $x \in R$.$k - \cos x \geq 0 \implies k \geq \cos x$.Since the maximum value of $\cos x$ is $1$,for $k \geq \cos x$ to hold for all $x$,$k$ must be greater than or equal to the maximum value of $\cos x$.Therefore,$k \geq 1$.

If $f(x) = kx - \sin x$ is monotonically increasing,then

Similar Questions

Which of the following functions is a strictly increasing function?

The interval for which the given function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is decreasing,is

Let $f(x) = x^3 + 6x^2 + px + 2$. If $f(x)$ is a decreasing function on the interval $(-3, -1)$,then $p = \dots$

The interval in which $y = x^2 e^{-x}$ is decreasing is . . . . . . .

If $f(x) = x + \log \left( \frac{x-1}{x+1} \right)$ is a well-defined real-valued function, then $f$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module