Please show all workings

Problem 4: Putting the Pieces Together (6 points) Now that we have calculated the derivative g'(x) for x = 4, x 4, we can summarize our results as a new piecewise function. Then we will use our formula to answer one more question about the derivative. a) (3 points) Fill in the blanks to write the derivative g'(x). (Hint: Watch your variable! We want g'(x), not g'(a).) if x 4 As you can see, the derivative g'(x) is a new function in its own right. And just like any other function, we can investigate its derivative, if it exists. b) (3 points) Use the skills you learned from Problems 1 and 2 to determine if the derivative of g'(x) exists at x = 4. If this derivatives does exist, find its value. If it does not exist, state this. Either way, EXPLAIN