Question

Prove that the function given by $f\left(x\right)=\cos x$ is strictly increasing in $(\pi ,2\pi )$.

Answer 1

Given $f\left(x\right)=\cos x$

$f^{{}^{\prime }}\left(x\right)=\frac{d}{dx}f\left(x\right)=-\sin x$

for $xϵ(\pi ,2\pi );\sin x<0$

$\Rightarrow f^{{}^{\prime }}\left(x\right)>0$

Hence $f\left(x\right)$ is strictly increasing in $xϵ(\pi ,2\pi )$