Problem. Let f be a function, let
a be in the domain of f, g(x) = m (x  a) + f(a) be the tangent line to the graph of f at
x = a. We know that the tangent line is an
approximation to f near x = a. The problem that we want to consider is how close
to a is g a good approximation to f. More precisely, given
e > 0,
the problem is to determine for what x near a is f(x)  g(x) < e?

