Module Six Discussion For this week's discussion, you are asked to generate a continuous and differentiable function f (@) with the following properties: . f (x) is decreasing at c = -6 . f (x) has a local minimum at = = -2 . f (x) has a local maximum at c = 2 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 (x). For example, one of the requirements is that f (-2) = 0 . If you want to find a function g (x) such that g (-9) = 0 and g (8) = 0, then you could try g(x) = (x+9) (x - 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 -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(@) = Save Quit & Save Previous Page Next PageIn Modules Four and Five. we studied the properties of functions, such as determining whether they are increasing or decreasing, and finding their maxima, minima. and concavity. We then put all of that together to sketch what the graph of the function looks like. In this discussion, we do the opposite. We start with what we want the graph of a function to look like and then try to find a function that has those properties. This type of problem is useful in design when we have a target end result (shape of the curve) and need to find a way to build something (a function) that leads to that target result. For example, this could be used in noise reduction where engineers remove static from sound. You are required to post one initial post and to follow up with at least two response posts for each discussion assignment. You should post your discussion response first. and then respond to other students. For your initial post (1]. you must do the following: . Before posting in this discussion, go to Mobius Module Six and complete the Module Six discussion activity. There you will be given certain properties that we want a function to have (increasing, decreasing. local maxima, etc.), and you need to find a function that has all of those properties. You can test out your solution with the graphing program in the Mobius Module Six discussion activity. In this discussion, we do the opposite. We start with what we want the graph of a function to look like and then try to find a function that has those properties. This type of problem is useful in design when we have a target end result (shape of the curve) and need to find a way to build something (a function) that leads to that target result. For example, this could be used in noise reduction where engineers remove static from sound. You are required to post one initial post and to follow up with at least two response posts for each discussion assignment. You should post your discussion response first, and then respond to other students. For yourinitial post (1], you must do the following: . Before posting in this discussion, go to Mobius Module Six and complete the Module Six discussion activity. There you will be given certain properties that we want a function to have (increasing, decreasing. local maxima, etc.), and you need to find a function that has all of those properties. You can test out your solution with the graphing program in the Mobius Module Six discussion activity. . In the Brightspace discussion, post the criteria that you needed to match and the function that you found in Mobius. Describe the process that you used to solve the problem in Mobius. . Complete your initial post by Thursday at 11:59 pm. of your local time