Is f(x)=x^a a Strictly Convex Function for a>1 on (0,\infty)?

  • Level: Graduate 
  • Thread starter Thread starter Edwinkumar
  • Start date Start date
  • Tags Tags
    Function
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
1 reply · 2K views
Edwinkumar
Messages
23
Reaction score
0
Is it true that [tex]f(x)=x^a[/tex] is always a strictly convex function for [tex]a>1[/tex] on [tex](0,\infty)[/tex]?
 
Physics news on Phys.org

Discussion

Similar threads

Graduate Existence of strictly convex functions with same ordering as convex one

  • Ed Seneca
  • · Replies 7 ·
  • Calculus
Replies
7

Prove: Integral Inequality for Convex Function

  • anemone
  • · Replies 1 ·
  • Calculus
Replies
1

Is the Minimum of a Strictly Convex Function Unique at Its Critical Point?

  • JS10
  • · Replies 2 ·
  • Topology and Analysis
Replies
2

Proving f(1 + w) > f(1) + w*f'(1) for convex functions

  • IlanSherer
  • · Replies 1 ·
  • Calculus
Replies
1

Q(x) is a strictly convex function, show that G is positive definite

  • numbersense
  • · Replies 2 ·
  • General Math
Replies
2

Proof involving convex function and concave function

  • TyroneTheDino
  • · Replies 6 ·
  • Calculus and Beyond Homework Help
Replies
6

Convex Functions: Find $f,g$ Satisfying f(x)=g(x) iff x is an Integer

  • evinda
  • · Replies 9 ·
  • Topology and Analysis
Replies
9

Graduate Proving Increasing Function of f(x)/x on ]0,∞[

  • LikeMath
  • · Replies 5 ·
  • Calculus
Replies
5

Convex Function on Many variables on an interval

  • curiousguy23
  • · Replies 2 ·
  • Calculus and Beyond Homework Help
Replies
2

Convex function on closed interval?

  • csc2iffy
  • · Replies 1 ·
  • Calculus and Beyond Homework Help
Replies
1