find constants a,b, and c such that the graph of will increase to the point , decrease to the point (1,-14) and then continue increasing
Set this equal to zero at the points and which will be our critical points.
We get and
Solving these simultaneous equations gives us...
You can check the second derivative to see that the points and are indeed a max and a min.
Hence we have .
Now just find a value of that solves...
(for the point ...)
Graph of said function below after you find the value...