In class, the following exercise was proposed.
Determine the natural cubic spline that passes through the points (0,1) (1, 0) (2, 0.5) (3, 1). Use the Hermite method
I need to interpolate a function, but to get it I need the slopes at those same points (that's to be able to use the method of divided differences, which is the only method I know). The exercise did not provide us with such data, that's where my question appeared. How do I get the slopes at those points? Or is there some other (Hermite) method that allows me to interpolate the function I need?
Any clue that helps me solve the exercise shown above would be of great help.