Answer:
See proof below
Step-by-step explanation:
We will use properties of inequalities during the proof.
Let . then we have that . Hence, it makes sense to define the positive number delta as (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 , then . First, then hence
On the other hand, then hence . Combining the inequalities, we have that , therefore as required.