<aside> 🔑 If f is continuous on a closed interval [a, b], then f has both a maximum value and a minimum value on the interval [a,b]

</aside>

Let’s identify what makes a function without a extrema.

• If there is function that a hole or discontinuity. There is always a value greater or lesser than the point we choose, as there is infinite points that is more closer than the point we close. (if there a increase or decrease toward the hole)
  • or we can view the hole as the peak that couldn’t exist because of the function’s domain.

However, there is no guarantee of the conclusion of no extrema if the condition of the theorem is not satisfy in the function.

• Think….
  • What if there is no increase or decrease toward the hole? y= x/x.
  • What if there is point of the highest or (and) lowest point is not the hole, but a random point is?
  • …..