Repeat Exercise 77 for the product function f(x) = x³(x − 3)².

Data from Exercises 77

Graph f(x) = x⁴ + 2x³ − x + 1 using a graphing utility with a viewing rectangle of [−5, 5]1 by [0, 2]0.5. Use TRACE and ZOOM, or the maximum and minimum commands, to find the minima and maxima of this function. Find the derivative function f'(x) algebraically, and graph f(x) and f'(x) on the same axes using a viewing rectangle of [−5, 5]1 by [−2, 2]0.5. Use TRACE and ZOOM or the zero command to find the x intercepts of f'(x). Explain why the maxima or minima of f(x) occurs at the x intercepts of f'(x).