Enroll in one of our FREE online STEM bootcamps. Join today and start acing your classes!View Bootcamps

University of California, Riverside

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 9

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)=1-\frac{4}{x^{2}}, \quad x \neq 0\end{equation}

Answer

$$

\begin{array}{l}{\text { (a) Critical points } x=\pm 2,0 |(b) \text { see the graph }} \\ {\text { (c) local maximum point } x=-2 \text { local minimum point } x=2}\end{array}

$$

You must be logged in to bookmark a video.

...and 800,000 more!

## Discussion

## Video Transcript

Okay, So for prom night, um, if the ribs were given ISS one minus four over X squared where asked Ex cannot be zero. So the first thing we need to do is to find the critical points that is to let the derivative to be equal to zero on DDE This case, we can find a solution, which is positive or negative too. Okay, now for party, let's first let the derivative to be positive now, by solving this inequality we can find. So the first thing we can do is to won't apply X squared on both sides. So that's X squared minus four, bigger than zero. So that means X squared is strictly bigger dead for hens. Our acts should be bigger than two or X. Be smaller than next to. So that means, um, like to be ability to thank you too. Union Two, two You been t on this interval function will be increasing and I think to to to his function will be decreasing. Oh, I'm sorry. Um, remember that we don't allow X to be zero, so we have to act. I have to exclude zero from this interval, so that means our our interval for decreasing will be from negative 2 to 0. Union 02 hostile to. Okay, now for Parsi. Now. See you. We need Thio. We need to find a local Mexico. My local minimum. Well, in this case, we observed these two intervals. Then we can find, uh, connected to we'll be the local maximum and half of two will be the local minimum.