Question

Define what it means for a function $f$ with domain $\mathbb{R}$ to have (a) a global minimum at $x=c$ and (b) a local minimum at $x=c$

Name: Problem 20, Chapter 0: Calculus
Uploaded: 2022-02-06T23:37:56-08:00
Duration: 2 min 50 s
Channel: Samriddhi Singh
Description: Define what it means for a function f with domain ℝ to have (a) a global minimum at x=c and (b) a local minimum at x=c

   Define what it means for a function $f$ with domain $\mathbb{R}$ to have (a) a global minimum at $x=c$ and (b) a local minimum at $x=c$

Calculus

Laura Taalman, Peter… 1st Edition

Chapter 0, Problem 20

Instant Answer

Solved by Expert Samriddhi Singh

02/06/2022

Step 1

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. In this case, the function $f$ has a domain of all real numbers, denoted as $\mathbb{R}$. Show more…

Show all steps

Thanks for your feedback!

Define what it means for a function $f$ with domain $\mathbb{R}$ to have (a) a global minimum at $x=c$ and (b) a local minimum at $x=c$

Play audio

Feedback

Samriddhi Singh and 57 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Global Minimum

A global minimum of a function is a point in the function's domain where the function attains its lowest possible value over the entire domain. Formally, a function f has a global minimum at x = c if for every x in the domain of f, f(c) is less than or equal to f(x). This means no other value in the domain has a function value lower than f(c).

Local Minimum

A local minimum is a point where the function attains its lowest value within some neighborhood around that point, rather than over its entire domain. Formally, f has a local minimum at x = c if there exists an interval (neighborhood) around c such that for every x in that neighborhood, f(c) is less than or equal to f(x). This property may hold even if there are lower values of the function outside of this neighborhood.

Please give Ace some feedback