If f is concave up around x = a, is the tangent line to f at a above or below the graph of f? What about if f is concave down?
If f is concave up, the tangent line to f at a is below the graph of f. This is true whether the slope of the tangent line is negative, zero, or positive.
The moral of the previous exercise is that when f is concave up, a tangent line approximation is an underestimate. Since Euler's method is a bunch of tangent line approximations stuck together, Euler's method will also provide an underestimate, regardless of how many steps are used
When f is concave down, a tangent line approximation is an overestimate. Since Euler's method is a sequence of tangent line approximations, Euler's method also provides an overestimate, regardless of how many steps are used.
Remember when we drew, on a slope field, solutions to a differential equation that passed through a particular point? If we can sketch a solution, we can tell whether it's concave up or concave down. That's all we need to tell whether Euler's method will overestimate or underestimate.