For each part, you$re$ given a function $f(x)$ and a closed interval $[a,b].$ First, find all critical points $off(x)$ over its entire domain, and not just over $[a,b](remember$ there are two types $of$ critical points$).$ Then, find the extreme values $off$ over $[a,b]$

$(a)f(x)=\frac{x^2}{x^2-4x+8}$;$[a,b]=[1,6]$

$(d)f(x)=4x-\sqrt[\phantom{2}]{x^2+1}$;$[a,b]=[-2,2]$

$(b)f(x)=\frac{x^2+1}{x-4}$;$[a,b]=[5,6]$

$(e)f(x)=si{n}^{-1}(x)-2x$;$[a,b]=[-1,1]$

$(c)f(x)=x-4\sqrt[\phantom{2}]{x+1}$;$[a,b]=[-1,5]$

$(f)f(x)=sin(x)+cos(x)$;$[a,b]=[0,\frac{}{2}]$