Which describes $f(x) = - 2 x + \sin x$ ?

Strictly increasing on

\mathbb{R}

Correct answerYour answerStrictly decreasing on

\mathbb{R}

Correct answerYour answerIncreasing on one part of

\mathbb{R}

and decreasing on anotherCorrect answerYour answerConstant on

\mathbb{R}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$f'(x) = \cos x - 2$ .
Here $\cos x \le 1$ , so $f'(x) \le -1 < 0$ , so $f$ is strictly decreasing on $\mathbb{R}$ .

Worth noting

A sine or cosine term wobbles, but a larger steady term decides the sign of $f'$ .

Ten questions from Increasing & Decreasing Functions, at your own pace.

Ten questions from Increasing & Decreasing Functions, at your own pace.

Which describes f(x)=−2x+sin⁡xf(x) = - 2 x + \sin xf(x)=−2x+sinx?