Suppose ƒ(a) = b and L(x) = b + m(x – a).

Suppose for all x in some open neighborhood of a we have

L(x) < f(x) if x < a and L(x) > f(x) if x > a.

Then m is **not too small** to be ƒ '(a).

In a similar way, we define what it means to say m is **not too big** to be ƒ '(a).

If just one number is not too small and not too big, then that number is ƒ '(a).