I need to find a function that can be proved using calculus techniques. I have used every local source of information to find a method to work this out but alas... the answer eludes me.
Heres the question:
Following 5 point lie on a function: (1,20) (2,4) (5,3) (6,2) (10,1)
Find an equation that passes through these points and has all the following:
3 points of inflection
At least 1 local minimum and local maximum
At least one Critical point (eg max/min/intercept etc) is not at a given point
The curve is continuous and differentiable throughout
The equation is not a single polynomial, but must be a piecewise-defined function
Now I know that theres gonna be many different functions. All I need is a method to work one out for myself. I am at a loss of how im meant to get this...
Thanks for any help provided
Crozius