1. calculate the 1rst derivative (use chain rule!):
You know that f'(0) = 0 and f'(5) = 0
Plug in these values into the equation of the derivative:
that means you can't determine the values of the parameters.
Since you know that at x = 5 is the next extremum you know that in this case k = 1 so
2. Plug in the coordinates of the points you know into the equation of the function:
3. Now you have a system of 2 simultaneous equations. Solve for A and C.
I've got A = 1.5 and C = 7.5
The equation of your function reads now:
I've attached a diagram of the graph.