a. We say that a function ƒ : [a,b] that f(x) < f(y) for every y € (x - Ďf(x) > 0 > Df(x). R has a local minimum at x if there exist h > 0 such h, x + h) n [a,b]. Show that, if x is a local minimum,
a. We say that a function ƒ : [a,b] that f(x) < f(y) for every y € (x - Ďf(x) > 0 > Df(x). R has a local minimum at x if there exist h > 0 such h, x + h) n [a,b]. Show that, if x is a local minimum,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please answer only 1st question with clear explation
![1. a. We say that a function f : [a, b] → R has a local minimum at if there exist h > 0 such
that f(x) < f(y) for every y e (x – h, x + h)n [a,b]. Show that, if x is a local minimum,
Df(x) > 0 > Df(x).
b. Let f be a continuous function [a,b]. Assume that Df > 0 for every x e [a, b]. Prove that f
is non-decreasing on [a,b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f27510b-2dba-4166-bbe5-25e12066f2e9%2F805ca64a-9b98-441e-bc59-76a55a0558e0%2Fn3fteu_processed.png&w=3840&q=75)
Transcribed Image Text:1. a. We say that a function f : [a, b] → R has a local minimum at if there exist h > 0 such
that f(x) < f(y) for every y e (x – h, x + h)n [a,b]. Show that, if x is a local minimum,
Df(x) > 0 > Df(x).
b. Let f be a continuous function [a,b]. Assume that Df > 0 for every x e [a, b]. Prove that f
is non-decreasing on [a,b].
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