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  4. Let f be the function f(x)= cos x-(1-(x2/2)) then f(x) is strictly increasing in the interval

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Q. 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

Application of Derivatives

Solution:

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