Let y = f (x) be a solution to the IVP
Does Euler's method produce an over- or under-estimate for the value of f (2)?
We left out the number of steps to use with Euler's method, but that doesn't matter for the answer. The slope field for looks like this:
Since the initial condition puts the solution under the line y = x, the solution is concave down:
Therefore that Euler's method will produce an overestimate.