> 
> Range of $f(x)=\cos^{8}x+\sin^{14}x\;\forall x \in \mathbb{R}$
> 
> 
> 

$\bf{My\; Try::}$ For upper bond::

Using $\sin^{14} x \leq \sin^2x$ and $\cos^{8}x\leq \cos^2 x$

So we get $$\sin^{14}x+\cos^8 x\leq \sin^2 x+\cos^2 x=1$$

So $\max$ of function $f(x)=1$ 

Now for lower bond::

$\sin^{14}x+\cos^8 x>0\;,$ Bcz $\sin^{14}x$ and $\cos^8 x$ can not $0$ simultaneously

My question is How can we calculate Minimum value of $f(x)\;,$ Help required, Thanks