For this week's discussion, you are asked to generate a continuous and differentiable function f(:1:) with the following properties - f(1) is decreasing at: : 6 - f(1) has a local minimum at :i: : 3 . f($) has a local maximum at :c : 3 Your classmates may have different criteria tor 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 (I) rst determine requirements for its derivative 1" (1:) For example, one of the requirements is that f, (73) : 0 , - If you want to nd a function 9(2) such that 9(79) = 0 and g(8) = 0, then you could try 9(1) : (35 +9)(1C , 5) - If you have a possible function for f'(1), 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 D07", Notice that the label "f (:5) =" 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 mantis go from b to 6, It is recommended that you put a multiplication symbol between variables or between a Variable and Tr (should you use it) Example: Write sin (1r - :0)instead of sin (7m), 0'90