Answer:
See proof below
Step-by-step explanation:
We will use properties of inequalities during the proof.
Let  . then we have that
. then we have that  . Hence, it makes sense to define the positive number delta as
. Hence, it makes sense to define the positive number delta as  (the inequality guarantees that these numbers are positive).
 (the inequality guarantees that these numbers are positive).
Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that  , and if we prove this, we are done. To prove it, let
, and if we prove this, we are done. To prove it, let  , then
, then  . First,
. First,  then
 then  hence
 hence  
 
On the other hand,  then
 then  hence
 hence  . Combining the inequalities, we have that
. Combining the inequalities, we have that   , therefore
, therefore  as required.
 as required.