For this week's discussion, you are asked to generate a continuous and differentiable function f (x) with the following properties: . f (x) is decreasing at x = -6 . f (a) has a local minimum at x = -3 . f (x) has a local maximum at x = 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 (), first determine requirements for its derivative f (). For example, one of the requirements is that f (-3) = 0 . If you want to find a function g (x) such that g (-9) = 0 and g (8) =0, then you could try 9 (x) = (x+9) (2 -8). If you have a possible function for f (a), then use the techniques in Indefinite Integrals this Module to try a possible f (I). 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 "f (x) =" 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 x-axis go from -6 to 6. It is recommended that you put a multiplication symbol between variables or between a variable and 7 (should you use it). Example: Write sin (7 . x )instead of sin (x). f (x) = sin (a)