Let such that
Find the values of the constants .
First, let’s compute the first and second derivatives,
Now, we start determining values based on the conditions given,
Next, using this value we have , so,
Then, plugging these values into the expression for we have
. So,
and,
Therefore,
The way I see it, this was done using a given 0 value that was used to figure out b, then c and so on. If those 0 values are given, this method works great. If they are not given, this method could most likely not be used. An alternative method is to set up a system of equations (with all given values), then isolating for a,b,c and d and solving.