Question

Let $f$ be the function $f(x)=\cos x-\left(1-\frac{x^2}{2}\right)$ then $f(x)$ is strictly increasing in the interval

• A. $(-\infty ,\infty )$
• B. $(-2,\infty )$
• C. $[0,\infty )$
• D. $(0,\infty )$

Answer 1

Answer: (A)

$f^{\prime }(x)\ge 0$
$\Rightarrow -\sin x+x\ge 0$
$\Rightarrow x\ge \sin x$
$\Rightarrow x\in [0,\infty )$