   Chapter 3.1, Problem 1E

Chapter
Section
Textbook Problem

# Explain the difference between an absolute minimum and a local minimum.

To determine

To explain:

The difference between absolute minimum and a local minimum

Explanation

1) Concept:

Use definitions of absolute minimum and local minimum.

2) Definitions:

i. Let c be a number in the domain D of a function f; then f(c) is the absolute minimum value of f on D if fcf(x) for all x in D

ii. The number fc is a local minimum value of f if fcf(x) when x is near c.

In local minimum, f takes the smallest value of f when x is near c

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