Show that the function `f(x)={:{(3+x", " xge0),(3-x", " x lt 0):}` is
not differentiable at x=0

Show that the function f(x)={:{(x^2+2", " xge1),(2x+1", " x lt 1 ):} is always differentiable at x=1

Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" "0", " x=0):} is not differentiable

Show that the function f(x)={x^msin(1/x), x=0 ,0 ,\ \ \ x!=0 ,\ \ \ \ \ \ \x=0 is differentiable at x=0 , if m >1

Show that the function defined by f(x) = {{:(x^(2) sin 1//x",",x ne 0),(0",",x = 0):} is differentiable for every value of x, but the derivative is not continuous for x=0

Show that f(x)=|x| is not differentiable at x=0 .

Show that f(x)=|x| is not differentiable at x=0.

The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made differentiable at x = 0

Show that the function f given by f(x) ={{:( x^(2)+5, if x ne 0), (3, if x = 0):} is not continuous at x=0

Show that the function f(x) ={:{((sin 3x)/(x)", "x ne 0),(1", " x= 0):}, is discontinuous at x=0.

Discuss the continuity of the function f(x) ={(x", " x ge 0),(2", "x lt0):} at x=0