Question

The function$x-cotx$

• A. always increases
• B. always decreases
• C. never decreases
• D. sometimes increases and sometimes decreases

Answer 1

The correct option is A

always increases

Explanation for the correct option

Given: $x-cotx$

Let $f\left(x\right)=x-cotx$

On differentiating w.r.t.$x$, we get

$f\text{'}\left(x\right)=1+\cos e{c}^{2}x$

as the range of $\cos ecx$function is $(\infty ,-1]\cup [1,\infty )$, the minimum value of the slope will be $2$ and it will keep on increasing.

Hence, the given function is always increasing, so, option (A) is the correct answer.