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.