Turn in #6 is due Friday, Oct. 24, 2014!
This is for discussing assignments from WEEK 7 & WEEK 8, including homework,
turn-in #6, MIDTERM REVIEW & QUESTIONS, and in-class work or lessons, or anything else related to the
class from this week. As this board covers two weeks, the maximum number of points will be 2 bonus points for participation. Please be sure to include your
name at the end of your post for credit. When answering a question, DO
NOT GIVE SOLUTIONS! Provide hints or explain a method that you used, but
do not give the final result. As always, RESPECT IS A MUST! Anyone
abusing this forum will be banned from future use (meaning, no extra
credit!!!).
DO NOT DISCUSS THE TAKE-HOME 1/2 QUIZ FROM MONDAY 10/13 ON THIS BOARD!!!!!
ReplyDeleteFor number 2c on the turnin, can a cusp be a point of inflection, because at x=2, there is a maximum so it should be a point of inflection but there is a cusp there, not a smooth curve.
ReplyDeleteThanks,
Emma Gijsbers
Well, let's refer to our definition of a POI, which is the function changes concavity at that x-value, which means the second derivative changes signs there. Thus, f" must be either zero or undefined at a POI. So, my question to answer your question is: is f" changing signs? If so, then...
DeleteNo, a cusp cannot be a point of inflection. There must be a smooth curve.
ReplyDeleteJ'Laan Pittman
On the turn in, for #1 how does the angle in part b change if you already cut it out in part a? Can you just subtract the angle from the overall circumference?
ReplyDeleteThanks,
Lexi Kizy
The way that I saw it was that a asked for the angle that maximized the volume of the cone created after sector was removed and that b asked for the angle that maximized the volume of the cone created by the sector itself.
DeleteJ'Laan Pittman
J'Laan is correct. It is the same theta for both parts, only the goal of part b is to maximize the cone that is created from the removed sector as opposed to the remaining sector. By the way, I highly encourage everyone to cut a circle out of paper and try making a physical model for this problem. It will help significantly!
DeleteI was looking back at the conCAVITY worksheet. For questions like 9 and 10, is it always true that any value of c and a works?
ReplyDelete-Safia Sayed
No, it is not ALWAYS true. But in the case of a polynomial, points of inflection will always occur at the midpoint of the interval between two consecutive extrema. Polynomials just aren't that interesting...
DeleteFor 2 E in the turn in, how to you get f"(x) also, does f''(x) have to be continous and differetiable in the interval aswell?
ReplyDeleteMarie Suehrer
You don't need to solve for f''(x)...the interval needs to be continuous and differentiable to use MVT and its not.
DeleteEva is correct. One thing to point out here (and the AP LOVES to do this) is that they are trying to apply MVT to f', so you need to think of f' as the function and f" as the derivative function here, if in fact you could use MVT.
Deletefor 4b on the turn in is it concave up even though g''(x) never curves back up?
ReplyDelete-Abby Siegal
I'm not sure what you mean by "g" never curves back up". If g">0, then g is concave up by definition.
DeleteTwo updates: Turn In #6 will be due Friday 10/24 instead of Wednesday 10/22. Also, we will have a quiz Tuesday 10/21 covering Sections 4.1-4.3 (classifying extrema, analyzing data/graphs of f' and f").
ReplyDeleteWill graphing calculators be allowed?
DeleteThanks,
Rachel Hersch
It is a non- calculator quiz
DeleteCan you use MVT on an open interval?
ReplyDeleteThanks,
Rachel Hersch
You need continuity on a closed interval and differentiability on an open interval.
Delete-Safia Sayed
Well, the value proven by MVT will belong to an open interval. Be sure both parts of the hypothesis are satisfied before applying MVT, though.
DeleteIs it sufficient to show a critical point is a minimum by sketching a simple graph of the derivative?
ReplyDeleteThanks,
Rachel Hersch
Yes. I do this sometimes in class to show how/why we know the sign is changing.
DeleteIn general, can Rolle's theorem be used in place of MVT unless otherwise specified?
ReplyDeleteThanks,
Allison Honet
No, Rolle's is a particular application of MVT that allows us to prove that there must exist a horizontal tangent on an interval. It is essentially using MVT on an interval whose end points have the same y value, so we get a secant slope of 0.
ReplyDeleteWill diagrams be given for the optimization questions on the midterm like they are given on the optimization worksheet we did in class?
ReplyDelete-Amanda Bachand
The AP likes to provide diagrams frequently. If there is little chance for ambiguity in the problem, then a diagram may not be provided (such as the distance from a curve to a point), but in most cases you will be given a diagram.
DeleteFor 5a on the turn-in, it asks for intervals on which f(x) is increasing. When writing the intervals, should we use brackets or parentheses?
ReplyDeleteThanks,
Jenna Weed
I would use parenthesis because at the endpoints of the intervals on which f(x) is increasing, the slope would be 0 and therefore neither increasing nor decreasing.
Delete-Daniel Honet
For number two on the turn-in, what is an acceptable amount of work to show in order to justify your answer? Are sentences okay or should the points be mathematically proven?
ReplyDeleteThanks,
Julia Berthel
There is no work to show, just justify your answer. Example: "x = c is a relative max because f' changes from positive to negative."
DeleteI think you are better off writing sentences. It's easier to write f' is changing signs from positive to negative or vise versa than it is to write the same thing using mathematical points.
DeleteRafey Rehman
On the turn in #2a the derivative function is linear so the original function is a parabola. Is a parabola considered concave up?
ReplyDeleteThanks!
Laura Goo
A quadratic can be concave up or down. Check the second derivative's sign.
DeleteWhen saying that a critical point is a minimum or a maximum, do we have to justify this by saying that the derivative is greater than or less than __ for __ interval?
ReplyDeleteYes, you should always justify that a critical point is a relative min or max by showing that f' changes signs or f" is positive/negative.
DeleteHow far should we simplify 1c?
ReplyDeleteFried
Are the answers to the review problems for the midterm online?
ReplyDelete-Eva A-L
No.
DeleteDo we need to know the derivative of all the inverse trig functions or just the ones we needed to know for the quiz (all, but sec^-1 and csc^-1)?
ReplyDeleteThanks,
Allison Honet
You only need to know the four I told you, but you should be able to recognize the other two, which is easy since they are the only ones with an absolute value.
DeleteOn the Midterm review sheet it says we need to know about jerk. Since we didn't go into much detail about it in class, I was wondering to what extent we need to know about it?
ReplyDeleteThanks,
Rachel Hersch
Simply that it is the derivative of acceleration, so the third derivative of position.
DeleteAs far as formulas go, for volumes etc., will be provided the ones we have been provided on the quizzes?
ReplyDeleteMarie Suehrer
I'm pretty sure we should know the basic formulas and everything that we should have memorized on previous tests.
Delete-Julia Trombley
Will diagrams for optimization problems be provided on the midterm like they were on the worksheet in class?
ReplyDeleteThanks!
Laura Goo
I think he said that complicated ones (like the boat rowing problems) will be, but simpler ones will not.
ReplyDeleteKai Selwa
These are kind of goofy videos but they do go over some of things we're going to need to know for the midterm. So stop stressing out for a little bit and good luck tomorrow guys!
ReplyDeletehttps://www.youtube.com/watch?v=P9dpTTpjymE
https://www.youtube.com/watch?v=uqwC41RDPyg
-Kelsey Nowak
"You only use logarithmic differentiation when you are trying to take the derivative of a variable raised to a variable power," is this statement true? And when exactly do you take the limit of both sides of the equation? Do both of these scenarios only occur when using L'hopital's rule?
ReplyDeleteRafey Rehman
I'm not sure if that;' the ONLY time, but it's the only situation I know of so far though. You set the equation equal to y and take the natural log of both sides to bring the variable exponent down as a coefficient. Then you can take the limit of both sides (which does nothing to the side with ln(y)). They can occur during L'hopital's rule, but they don't have to.
ReplyDeleteThis board is now closed for earning bonus points. You may comment on the week 10 board if you have any HW questions from this week (after the midterm). Turn In #7 will be given out on Monday and will be due on Monday 11/10/14.
ReplyDelete