Question

Let I be an open interval, and f : I -> R differentiable, with f ′ differentiable and f ′′ continuous (i.e. f in C2(I)). Show that if there is x0 in I such that f ′′(x0) > 0 and f ′(x0) = 0, then x0 is a local minimum

Name: let i be an open interval and f i r differentiable with f differentiable and f continuous ie f in c2i show that if there is x0 in i such that f x0 0 and f x0 0 then x0 is a local minimum 35844
Uploaded: 2021-07-19T22:02:50-08:00
Duration: 1 min 6 s
Channel: Carson Merrill
Description: let i be an open interval and f i r differentiable with f differentiable and f continuous ie f in c2i show that if there is x0 in i such that f x0 0 and f x0 0 then x0 is a local minimum 35844

          Let I be an open interval, and f : I -> R differentiable, with f ′ differentiable and f ′′
continuous (i.e. f  in  C2(I)). Show that if there is x0  in  I such that f ′′(x0) > 0 and
f ′(x0) = 0, then x0 is a local minimum

Added by Steven E.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Carson Merrill

07/19/2021

Step 1

We have a function \( f: I \to \mathbb{R} \) where \( I \) is an open interval. The function \( f \) is twice differentiable on \( I \), meaning \( f' \) exists and is differentiable, and \( f'' \) exists and is continuous. We are given that there exists a point Show more…

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Let I be an open interval, and f : I -> R differentiable, with f ′ differentiable and f ′′ continuous (i.e. f in C2(I)). Show that if there is x0 in I such that f ′′(x0) > 0 and f ′(x0) = 0, then x0 is a local minimum