Problem

a. Identify the function's local extreme values i…

02:29

Problem 43 Easy Difficulty

a. Identify the function's local extreme values in the given domain, and say where they occur.
b. Which of the extreme values, if any, are absolute?
c. Support your findings with a graphing calculator or computer grapher.
$$
g(x)=x^{2}-4 x+4, \quad 1 \leq x<\infty
$$

Answer

See the graph

Topics

Applications of the Derivative

Book Cover for Thomas Calculus

Thomas Calculus

Chapter 4

Applications of Derivatives

Section 3

Monotonic Functions and the First Derivative Test

Discussion

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Watch More Solved Questions in Chapter 4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Video Transcript

and the function, which is G X, defined as X squared minus four x does war. So for part Elvis problem, we need to check the extreme that local extreme values. To do that, we first take the derivative of the function, which is to X minus four, and we let this rip him to be zero we can't solve for X, though axes to that it means G too. He's a local extreme value. But for part B, we need to identify whether this extreme value local stream batteries Absolute. Now we call that shape of this function is a rebel A and the only route is too. So the function should be looked like be like this and the domain is from one to infinity. So let's say this one. And until infinity we have the increasing function from 2 to 20. So have to will be our absolute minimum. So after is absolute or cheat you sorry. Due to its absent

Runpeng L.

University of California, Riverside

Topics

Applications of the Derivative

Book Cover for Thomas Calculus

Thomas Calculus

Chapter 4

Applications of Derivatives

Section 3

Monotonic Functions and the First Derivative Test

Top Calculus 1 / AB Educators

GH

Grace H.

Numerade Educator

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Joseph L.

Boston College