Welcome to this post on a topic in calculus and analysis!
Here, we'll discuss a key concept.
Let \( f \) be a continuous real-valued function on a closed interval \([a, b]\). Then, \( f \) attains both its maximum and minimum on \([a, b]\).
If \( f \) is differentiable on \([a, b]\) and \( f'(x) = 0 \) for all \( x \in [a, b] \), then \( f \) is constant on \([a, b]\).
Recall that in previous lessons, we explored the concept of continuous functions and their behavior on closed intervals.