`F(x) =x^3-3x^2+6` and `g(x)= max{F(t):x+1<=t<=x+2} -3<=x<0` and `1-x` for `x>=0` Find continuity and differentiability of g(x) for `x in [-3,1]`

Let f(x)=x^3-3x^2+6AAx in R and g(x)={m a x :f(t ; x+1lt=tlt=x+2,-3lt=xlt=0 1-x ,xgeq .Find continuity and differentiability of g(x) for x in [-3,1]

Let f(x)=x^(3)-x^(2)-x+1 and g(x)={max{f(t);0<=t<=x},0<=x<=1,3-x,1<=x<=2 Discuss the continuity and differentiability of the function g(x) in the interval (0,2).

Let f (x) = x^3-x^2-x+1 and g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, 1<=x<=2 Discuss the continuity and differentiability of the function g (x) in the interval (0, 2).

If f(x)=x^(2)-2|x|, then test the continuity and differentiability of g(x) in the interval [-2,3], where g(x)=min{f(t):2<=t<=x},-2<=x<0 and max{f(t):0<=t<=x,0<=x<=

Let f(x) = x^3-x^2 + x + 1 and g(x) = [max{f(t):0<=x<=x}, 0<=x<=1 and 3-x, 1

If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x) = f(|x|) + |f(x)| . Discuss the differentiability of g(x).

If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x) = f(|x|) + |f(x)| . Discuss the differentiability of g(x).

If f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x) = f(|x|) + |f(x)| . Discuss the differentiability of g(x).

If f(x)=(x+3)/(x-3) and g(x)=(1)/(x-7), then discuss the continuity of f(x),g(x) and fog(x)