What Are Local Minimum and Maximum Points in Continuous Functions?

  • Thread starter Thread starter sergey_le
  • Start date Start date
  • Tags Tags
    Minimum Point
Click For Summary
Local minimum and maximum points in continuous functions are discussed, focusing on the relationship between them. It is established that if a continuous function has a local minimum at x1 and a local maximum at x2, with f(x1) > f(x2), then there must exist another local minimum point. The Extreme Value Theorem is referenced to support the existence of this additional minimum within the interval [x1, x2]. The conversation emphasizes the need for a rigorous argument to show that this new minimum is distinct from x1 and x2. Ultimately, the discussion highlights the importance of careful definitions and theorems in proving properties of continuous functions.
  • #31
Thank you all so much you wonderful and patient people, I am glad I found this forum you are really helping me. Blessed
 
  • Like
Likes PeroK

Similar threads

Why is f Integrable on [a, b]?
  • · Replies 11 ·
Replies
11
Views
2K
Calculating Instantaneous Rate of Change for a Quadratic Function
  • · Replies 8 ·
Replies
8
Views
2K
Calculate this Integral around the Circular Path using Green's Theorem
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Open interval or Closed interval in defining convex function
  • · Replies 4 ·
Replies
4
Views
3K
Proving Div(x/|x|^2) = 2πδ(0,0) in 2D with Distribution Derivative
  • · Replies 14 ·
Replies
14
Views
2K
Derivative of multivariable function
  • · Replies 5 ·
Replies
5
Views
2K
Using an ODE to show a local minimum
  • · Replies 5 ·
Replies
5
Views
2K
Optimizing Functions: Strategies and Considerations
  • · Replies 8 ·
Replies
8
Views
2K
Can this function still be a constant function?
  • · Replies 11 ·
Replies
11
Views
2K
Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K