Segment One Collaboration Assessment Fill in the blanks for the free-response question to create your original problem. Please use the examples for inspiration but be sure to choose your own functions and values. Your Name: Partner's Name: Free-Response Question Let f be the function given by f(x) = (create an original polynomial of degree 3 with at least 3 terms). ex: f(x) = x3 - 4x2 + x + 2 Part A: Find f'(x). Part B: Write an equation for the line tangent to the graph of fat x = (integer value). ex: x = 2 Let g be the function given by g(x) = (create an original polynomial of degree 2 with at least 2 terms). ex: g(x) = x2 + 5x + 6 Part C: Find the average rate of change of g on the interval [-4, 4]. Part D: Write an equation for the normal line to the curve of g at x = [integer value) ex: x = 2 Part E: Let k(x) = f(g(2x)). Find k'(-1). Let h be the function given by h(x) = (create a piecewise function with no more than one piece being a linear function).Part F: Using correct mathematical notation, explain the differentiability and continuity of the piecewise function h(x). Partner's Solution to the Free-Response Question: Part A: Part B: Part C: Part D: Part E: Part F:Rubric with Scoring Comments Rubric Score & Comments Part A: Total: 1 point 1 point: One point is earned for correctly finding f'(x). Part B: Total: 2 points 1 point: The first point is earned for correctly finding the slope at f'(x), using the integer value chosen for x. 1 point: The second point is earned for writing the correct equation of the line, using (x, f(x)) as the point and f'(x) as the slope. Part C: Total: 1 point 1 point: One point is earned for correctly finding the average rate of change on [-4, 4]. Part D: Total: 2 points 1 point: The first point is earnedfor correctly nding the slope {the negative reciprocal} at g'ix}, using the integer value chosen fer x. 1 point: The second point is earned for writing the correct equation of the line, using (1', E!\" as the point and f '{x} as the slope. Total: 1 point 1 point: One point is earned for correctly using the Chain Rule to nd k'{-1). Total: 2 points 1 point: One point is earned for correctly proving if the function is continuous with accurate justication. 1 point: One point is earned for correctly proving if the function is differentiable with accurate justication