Show that the function 
is continuous but not differentiable at x=3.
Let c be a real number.
Case I: c<3 Then f(c) = 3-c.
CaseII: c = 3. Then f(c) = 3 - 3 = 0
Since
f is continuous at x = 3.
Case III: C>3. Then f(c) = c - 3
Since,
Therefore, f is a continuous function.
Now, we need to show that
Consider the left hand limit of f at x = 3
Consider the right hand limit of f at x = 3
Since the left and right hand limits are not equal, f is not differentiable at x = 3.
Switch
is equal to
