Georgia Southern University

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

Problem 2

Answer the following questions about the functions whose derivatives are given:

\begin{equation}\begin{array}{l}{\text { a. What are the critical points of } f ?} \\ {\text { b. On what open intervals is } f \text { increasing or decreasing? }} \\ {\text { c. At what points, if any, does } f \text { assume local maximum and }} \\ \quad {\text { minimum values? }}\end{array}\end{equation}

\begin{equation}f^{\prime}(x)=(x-1)(x+2)\end{equation}

Answer

$$

\begin{array}{l}{\text { (a) Critical points } x=-2,1 ](b) \text { see the graph }} \\ {\text { (c) local maximum at } x=-2, \text { local minimum at } x=1}\end{array}

$$

You must be logged in to like a video.

You must be logged in to bookmark a video.

## Discussion

## Video Transcript

So you're giving the derivative of a function F Crime of X is explain this one times X plus two. And so let's find the critical points of that. Well, these are the values of X through its theft crime of X zero Cor, undefined. But this derivatives never going to be undefined Soon X equals one and X equals negative to our critical points who just plug in one a negative to those will be the values vex to make of prime zero. Okay, And then we want to know All right, what values is f increased, their decreasing. Well, that's just asking it. What values Andi or what Open intervals is f prime, positive or negative. So you know, the F prime will potentially change sign at the critical points. So put not just to you here and one here and no test f prime so that blogging something smaller the negative to this factor is negative. This factor will be also negative, said F prime will be positive. And then, if I plug in and value between you two and one, this factor will be negative, and this factor will be positive. So the drip it it'll connective. And then if X is bigger than one and bigger than to both of these factors were positive. And so what that means for Earth is that ofthis increasing here, Decreasing here, increasing here. So it's increasing on this interval. Negative infinity. It's a negative, too decreasing between aged two and one and then increasing between one and infinity. All right, And then at what points does f assume local maximum minimum guys So it looks like here have changes from being increasing to decreasing. So hey, we have a local max at X equals negative too. And then we have a local men because of changes from decreasing to increasing at X equals one. Then a pre just sort of visualize what that looks like. It's increasing and decreasing that increasing. So we have a local max in the community.

## Recommended Questions