at x=3 the function given by
f(x)= x^2 , x<36x-9 , x ≥ 3is the function both continuous and differentiable?
Rule I: If you do not know the meaning of words in a problem, do not even start on the problem until you have looked up those words!
No, just being "defined" at a point does not mean a function is continuous or differentiable at that point. What is the definition of "continuous"? What is the definition of "differentiable"?