Before I begin, I must say that reading and quickly understanding the definitions of mathematical theorems is not my strongest suit.

We had a test where one of the subjects was Eulers methods. The problems we have in our study book (Adams and Essex) are problems that I felt went relatively easy, but on this test we encountered an even worse problem. The problem is:

The function f(x) is differentiable with a continuous derivative f'(x).

Some of the values of this derivative is listed in the table below:

(I will not list them now, but there is a row for values for x and what the value of f'(x) will be if you substitute this x with the value above. I'm not quite sure if I explained this well, but I hope someone gets the picture).

Furthermore, the problem says:

Suppose that f(1.4) = -0.9. Use Eulers method with stepsize h = 0.2 to find an approximate value for f(2.0).

This is the task. I'm not looking to have the problem solved for me, I only wish to understand the method of how I can solve this task. In my calculus book, the problems tied to Eulers method has contained a function, while in this problem it seems we have to figure out what the function is.

Thank you so much in advance if anyone replies.