For this week's discussion, you are asked to generate a continuous and differentiable functionf(x)

with the following properties:

• f(x) is decreasing atx=6
• f(x) has a local minimum atx=3
• f(x)has a local maximum atx=3

Hints:

• Use calculus!
• Before specifying a functionf(x), first determine requirements for its derivativef(x) For example, one of the requirements is thatf(3)=0.
• If you want to find a functiong(x) such thatg(9)=0 andg(8)=0, then you could tryg(x)=(x+9)(x8).
• If you have a possible function forf(x), then use the techniques in Indefinite Integrals this Module to try a possiblef(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 check 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 thex

-axis go from -6 to 6.