For this week's discussion, you are asked to generate a continuous and differentiable function f (:12) with the following properties: - f(.1:) is decreasing at as : 5 - f($) has a local minimum at m : *3 - f (x) has a local maximum at :1; : 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(a:), first determine requirements for its derivative 1'" (3:). For example, one of the requirements is that f, (*3) : 0 . If you want to find a function g (as) such that 9(79) : 0 and g (8) : 0, then you could try g(a:) : (.17 + 9) (m i 8). - If you have a possible function for f" (:c), then use the techniques in Indenite Integrals this Module to try a possible f(a:). 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 (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 maxis go from 6 to 6. fw: aha