`f(x)=x^2-2|x|,g(x)=min f(t):0 le t le x ,-2 le x le 0 and max f(t): 0 le t le x ,0 le x le 3` Sketch the graph of `g(x)` and discuss its differentiability

If f(x) = x^(2) - 2|x| and g(x) = {{:("min{f(t)":-2 le t le x",",-2 le x le "}"),("max {f(t):"0 le t le x",",0 le x le 3"}"):} (i) Draw the graph of f(x) and discuss its continuity and differentiablity. (ii) Find and draw the graph of g(x Also, discuss the continuity.

If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) is not differentiable at:

Let f(x)=f_1(x)-2f_2 (x), where ,where f_1(x)={((min{x^2,|x|},|x|le 1),(max{x^2,|x|},|x| le 1)) and f_2(x)={((min{x^2,|x|},|x| lt 1),({x^2,|x|},|x| le 1)) and let g(x)={ ((min{f(t):-3letlex,-3 le x le 0}),(max{f(t):0 le t le x,0 le x le 3})) for -3 le x le -1 the range of g(x) is

Find the area of region {(x,y):0leylex^(2)+1, 0 le y le x+ 1, 0 le x le 2} .

Let f(x)=f_(1)(x)-2f_(2)(x), where f_(1)(x)={{:(min{x^(2),|x|}",",|x|le1),(max{x^(2),|x|}",",|x|gt1):} "and "f_(2)(x)={{:(min {x^(2),|x|}",",|x|gt1),(max{x^(2),|x|}",",|x|le1):} "and let "g(x)={{:(min{f(t),-3letlex,-3lexlt0}),(max{f(t),0letltx,0lexle3}):} The graph of y=g(x) in its domain is broken at

Let g(x)= f(x) +f'(1-x) and f''(x) lt 0 ,0 le x le 1 Then

If f (x) =x ^(2) -6x +5,0 le x le 4 then f (8)=