At `x=0`, function `f(x)={x^3(1-x) , x leq 0 and xIn x+3x , x lt 0`

If function defined by f(x) ={(x-m)/(|x-m|) , x leq 0 and 2x^2+3ax+b , 0 lt x lt 1 and m^2x+b-2 , x leq 1 , is continuous and differentiable everywhere ,

Check whether the function f (x) = {{:(3 + x if x ge 0), ( 3-x if x lt 0):} is differentiable at x =0.

If f(x)={(x^3, x gt 0),(0, x=0),(-x^3, x lt0):}

Discuss the continuity of the function f(x) ={:{((Sinx)/(x) ", "x lt0 ),(x+1 ", " x ge0):}, at =0.

Discuss the continuity of the function f(x) ={:{((Sinx)/(x) ", "x lt0 ),(x+1 ", " x ge0):}, at =0.

Prove that the function f(x)= {((sin 3x)/x", " x lt 0),(x+3 ", " x ge 0 ):} is everywhere continous .

Prove that the function f(x)= {((sin 3x)/x", " x lt 0),(x+3 ", " x ge 0 ):} is everywhere continous .

A function defined by f(x)=x+a for x lt 0; x for 0 leq x lt 1; b-x for x geq 1 is continuous in [-2,2]. Show that (a+b) is even