Question:

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

• f(x) is decreasing at x=5
• f(x) has a local minimum at x=3
• f(x) has a local maximum at x=3

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 functiong(x) such that g(9)=0 and g(8)=0 then you could try g(x)=(x+9)(x8).
• if you have a possible function for f(x) then use the techniques in indefinite integrals this module to try a possible f(x).

Please note that the bounds of the x-axis go from -6 to 6.