Finding a Function to Match a Current Grade: 0.0/1.0 Remaining Time: Unlimited Shape 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(x) 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(x), first determine requirements for its derivative f ′
(x). 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 g(x)=(x+9)(x−8). - If you have a possible function for f ′
(x), then use the techniques in Indefinite Integrals this Module to try a possible f(x). 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 .
