Find the maximum and minimum values of the following function:

$f\left(x\right)=4x^3-15x^2+12x-2$

Find the maximum and minimum values of the following function:

$f\left(x\right)=x^3-9x^2+24x-12$

Find the maximum and minimum values of the following function:

$f\left(x\right)=\frac{x^2-7x+6}{x-10}$

Find the local maximum and minimum values of the function:

$f\left(x\right)=\frac{1}{x^2-3x+2}$

Show that: $\sin x<x<\tan x$ for $0<x<\frac{\pi }{2}$

Show that : $\log \left(x+\sqrt{1+x^2}\right)>{\tan }^{-1}x$ for $x>0$

Show that : $2x>{\tan }^{-1}x+\log \left(x+\sqrt{x^2+1}\right)$ for $x>0$

Show that : $\frac{1}{4}<{\sin }^{6}x+{\cos }^{6}x<1$ when $\frac{\pi }{4}<x<\frac{\pi }{2}$.

Show that: $\sin x+\tan x>2x$, for $0<x<\frac{\pi }{2}$.