SA #113

I. f(a) = f(b), not necessarily true
II. c is a relative extrema, also not necessarily true
III. c is a POI, also not necessarily true

OPENER NINE ("opener nine" in Webdings)

Hi, this is Kimmy.
I'm trying to correct my openers, but I don't know the answers to Opener #9. Does anyone have the answers to Opener #9?

Major Help

Hi, this is Priya.
I think a lot of people need help on #27. If somebody knows how, could you please explain. If not, Mrs. Carlson could you help us. Thanks!

Hw review help

This is Jennifer.
How do you do #22,24,27?
I am lost with these problems.

Calc A. Chapters 1-4 Review Worksheet Questions

Hi, this is Joyce, and I need major help.
For number 11, I got the x-values but I couldn't get the values. Don't you just graph y=4 and y=sec^2(x)?
Also, for number 16, I Ln'ed both sides, but I still can't get the answer.
Last one! For number 27, is it supposed to be h/r = (12-h)/5?
Your help is appreciated
Thanks :)

Glad to be back

Don't know about you, but I'm glad I'm back. I hope that we can catch up on what you're having trouble with tomorrow. I know it may seem like I'm rushing, but I don't think that what I'm asking for is impossible. Much of what we do now will spiral in with other things we will do later. It'll all come together. Promise.
It's nice to be back.

HW #8 number 8 d

Hi! This is Jean! ^__^
I need help on HW#8 Linearization question number 8 (d).
Where does the square root of 2 came from? o.O

Correction to HW#6 answers

I messed up. I had some mistakes on my answers. I'll be reposting in a short while on our edline page. So check back, okay?

BTW, on Monday and Tuesday, you'll have a sub, Mrs. Tse, who CAN TEACH YOU CALCULUS!!! So bring your questions to class, okay!?

From Hannah (with my answers embedded in between)

Dear Mrs. Carlson,
I tried to post my questions to the homework on the blog, but I don't know how. Here are some of my questions in regard to the f' and f'' hw.

1. Do Max's and Min's include pointy points (like question number 4 in the inclass examples) because Mrs. Cordova said that the pointy ones are not max's or min's since they can have more than one tangent line?

Go can look at the Formulas and Theorems worksheet I asked you guys to print out. Look at #11, on page 5. Relative extrema can occur when the derivative is zero OR undefined.

2. On question 4f (in class exercise again), why isn't 3 a point of inflection? Isn't the point of inflection the point at which the concavity changes?

Because for there to be a POI at x=3, f'(x) must also exist at x=3, which it doesn't. This is a part that many people forget. Not only does there have to be a change in concavity, the first derivative must also exist there.

3. Question 4 (in class), for the interval (3, to infinity), shouldn't the graph of f' become steeper since the slope of f(x) is becoming steeper?

Yes, you are right. I should have drawn something that is decreasing on that interval. Possibly a hole at (3,0) and decreasing as it goes towards infinity.

4. Question 5 (hw), why aren't -1 and 1 answers for question f?

Same as your question above. First derivative doesn't exist at x=1, 1.

5. Question 7, how is 0 a max/min? (pointy?)

Same as above. f' = undefined still qualifies the point as relative extrema.

6. Question 6, from the answer sheet, i dont understand the part when you wrote (x=1) if you have f' existing there.

I interpreted the graph such that there would be a vertical tangent line at x=1. If that is true, then the first derivative does not exist there (therefore no POI).
If you interpreted the graph so that there ISN"T a vertical tangent line at x=1, then the first derivative DOES exist, which means there you WILL have a POI there.

7. Question 8, dont inflection pts include -1, 2, and 5 as well?

Again, similar to the one above. I treated those all as vertical tangent lines...therefore no POI. Since I wasn't there to clarify, if you DIDN'T consider them to be vertical tangent lines, then yes, you would have 3 POIs there.

If you have time, please answer my questions. Thank you. I miss you.

I miss you guys, too!

Sincerely,
Hannah

Just wondering...and hw #6 question

Hello Mrs. Carlson! This is Jennifer Oh :)
When are you coming back?
It's hard to learn things thoroughly without you here to lead us.
I hope you can come back soon.

And, is there an easier way to sketch the graphs of f' and f''? Or do we just have to work our way through step by step?
How do you draw the sign charts of f' and f''? What numbers are the points for the sign charts: the zeros, undefined points?

HW#6 Solutions

They are posted on our edine page.
Bring your discussions here. But I'd like for you guys (the students) to talk it out with each other. Can we try that?

Questions on Summer Assignments answered...

#61. This is actually an optimization problem. Using the distance formula, write out the equation using the point given and also substitute in for y using the equation of the curve. This way you'll have an equation with only D and x. I suggest squaring both sides, because it will make taking the derivative much easier. Find find when dD/dx = 0.

#85. Use the sum and difference formulas for cosine to expand the numerator. Many of the terms will cancel out, and you can simplify nicely. You should then have something recognizable that you can evaluate the limit.

#91. This one always eludes many. Speed (a scalar) is the absolute value of velocity (a vector, meaning it has direction). So graph the absolute value of the velocity function and find the maximum.

#93. Look at the graph of the derivative and then go through the answer choices. (A) is false because the derivative is an odd function, which makes f even. (B) is also false because if f is always increasing, then that means the graph of the derivative must always be positive (above the x - axis). (C) is true because it only goes from negative to positive at the origin. (D) is false because the graph of f ' has a slope of zero (meaning f '' is zero) that means we have a POI. (E) is negative to the right of x = -(Pi), so the function is decreasing. It's not a minimum.

#94. Graph the function on the viewing window: [-4, 2] x [0, 1]. Look to see how many POIs you have.

Opener #1 (which you took as #2)

When it says find the value of k for which f has 11 as its relative minimum:
You need to use your answer from part (a) here. In part (a), you figured out the intervals where the function in increasing. You most likely also drew a sign chart, and from that, you should be able to see where a minimum occurs. This occurs when x = 3. This means that f (3) = 11. Because we are told 11 is it's relative minimum (value). This minimum occurs when x = 3. Plug the numbers in to find k.

Graphs of f from f' worksheet answers on Edline

Per student request, I will be posting the solutions on edline. I'll have to scan it in, and it'll be up as a .pdf file.

Updated Calendar on Edline

Sorry guys, I forgot to update the calendar online to reflect the changes since I've been out. Some of you have probably been a bit confused as to which HW problems you are supposed to be working on. Here's a quick recap of what it should be:
Wed 9/12: HW#7 Max/Min
Thu 9/13: HW#5 Graphs of f from f'
Fri 9/14: SA Discussion/Review
Mon 9/17: HW#9 Related Rates
Tues 9/18: HW#10 Related Rates
Wed 9/19: HW#6 Linearization
Thu 9/20: HW#8 Graphs of f' and f'' from f
Fri 9/21: HW#11 Related Rates
--then we're back on track--

One last thing. I'll be writing up some notes and examples for you on Related Rates so that you'll have some problems to refer to. The first day should have fairly straight-forward ones for you, with the problems getting a bit more complex the following day.

Max/Min

How are you guys doing with the max/min problems? I'm sorry I didn't have a chance to prepare any notes for you. I would've done some examples with you in class; but I didn't even have time to write them up, much less make the copies.
I think, if memory serves me right, there's a pretty tricky one with the girl rowing to the pier/walking along the shore?! What do you think about that one?

A couple more things...

As long as you register with blogspot, you can post a comment. But in order to post something, you'll need to let me know the email address you use so I can 'add' you in.

In case you are concerned about the 30-day trial of MathType. We are in the process of getting a new school license. Once we do, students are also allowed to use the program. So be patient and we'll have that soon.

Welcome!

I've created this blog to help facilitate discussions. Participation in discussions about topics covered in class, or problems and questions that you may have on homework is encouraged. What is the potential reward, other than the obvious? Constructive participation may raise a grade, should your grade fall on the borderline.
In order for you to post equations such as my little limit below, you'll need to do a couple of things. First, go to www.dessci.com and download a free 30-day trial of Mathtype6.0. You will then be able to save them as little .gif files and then upload them to the post. Capisce?

Oh yeah. One more thing. In order for you to be able to post to this blog, you'll need to send me and email with the address that you want to use (I have to add in your email address into this to give you permission). Only then will you be able to participate. So hopefully, that's everyone!