2 pts Let fR R be differentiable We say that f is convex if for...
90.2K
Verified Solution
Link Copied!
Question
Calculus
2 pts Let fR R be differentiable We say that f is convex if for all x y R and all t 0 1 f tx 1 t y tf x 1 t f y i e that the graph of f is below its chords a 1 pt Prove that f is convex if and only if f y f x Vf x y x for all r y R i e the graph of f is above its tangent lines b 0 5 pt Assume that f is C Prove that if f is convex then n fax x h h 20 i j 1 for all x h ER We recall that for a function g R R twice differentiable we have the following Taylor formula for all a b E R there exists c a b such that g c 2 This is no longer true for functions of several variables c 0 5 pt Applying the previous formula to the function g t f x th between a 0 and b 1 prove the reverse implication in the g a g b g b a b
Answer & Explanation
Solved by verified expert
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
