Suppose that you want to maximize the value of the function f(x) = x^3-6x^2+9x, subject to 0 less than or equal x less than or equal 5.
(a) Which value(s) of x satisfy the first-order condition for this maximization problem?
(b) Which value(s) of x are boundary points?
(c) Which value(s) of x solve the maximization problem?
(d) What is the maximized value of the function?
Now suppose you want to minimize the value of the function, subject to 0 less than or equal x less than or equal 5.
(e) Which value(s) of x solve the minimization problem?
(f) What is the minimized value of the function?