For this week's discussion, you are asked to generate a continuous and differentiable function f (:13) with the following properties: - f (:13) is decreasing at a: = 6 - f(:1:) has a local minimum at :1; = 3 - f(:1:) has a local maximum at a: = 3 Your classmates may have different criteria for their functions, so in your initial post in Brightspace be sure to list the criteria for your function. Hints: Use calculus! Before specifying a function f (:13) first determine requirements for its derivative f, (:12). For example, one of the requirements is that f, (3) = 0 . If you want to find a function 9 (ac) such that g (9) = 0 and g (8) = 0, then you could try 9 (w) = (:L' + 9) (a: 8). - If you have a possible function for fl (:13), then use the techniques in Indefinite Integrals this Module to try a possible f (2:). You can generate a plot of your function by clicking the plotting option (the page option with a "P" next to your function input). You may want to do this before clicking "How Did I Do?". Notice that the label "1' (m) =" is already provided for you. Once you are ready to check your function, click "How Did I Do?" below (unlimited attempts). Please note that the bounds on the :c-axis go from -6 to 6. rm: awn