6. If f(x) = x89 - 2x56 + 7x + er, find f(100) (x). (Remember, f(") (x) is the nth derivative of f(x). This is clearly a trick, I am not asking you to actually take 100 derivatives. Take moment and think about what will happen after 100 derivatives. It may help to take 5 derivatives of f(x) = x3 to start seeing a pattern. ) 7. A function is differentiable if it and its derivative are continuous. Define g(x) as the function below: 2x if x 2 (a) Take the derivative of each piece of the function. Determine if this new derivative is continuous at r = 0 and x = 2. (b) Sketch the graphs of g and g' on the same set of axes