For this week's discussion, you are asked to generate a continuous and differentiable function f(x)fx with the following properties:

• f(x)fx is decreasing at x=6x=-6
• f(x)fx has a local minimum at x=2x=-2
• f(x)fx has a local maximum at x=2x=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(x)fx, first determine requirements for its derivative f(x)fx. For example, one of the requirements is that f(2)=0f-2=0.
• If you want to find a function g(x)gx such that g(9)=0g9=0and g(8)=0g8=0, then you could try g(x)=(x+9)(x8)gx=x+9x8.
• If you have a possible function forf(x)fx, then use the techniques in Indefinite Integrals this Module to try a possiblef(x)fx.