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