Tuesday, April 15, 2008
BOB
Well, this unit about derivatives isn't too difficult considering that i learned this before. The only thing that i need to be careful on is working too fast for my own good. I usually make most of my mistakes on being too overconfident, but just to make sure I'll go over the orange and blue book tonight. Hopefully, i manage to get a good mark. Good luck everyone and study hard.
[B]logging [O]n [B]logging
Tomorrow is the test! Wow it's quite surprising how so many people have dropped this course throughout the minor portion of what has passed. Well, tomorrow is the test on Derivatives! It shouldn't be too difficult to be honest, especially for the AP Calc Students who have already learned this unit. Though I understand the most part of this unit, I know that I may still stumble somewhere, as questions are always different: there are always new wrinkles that you can run into.
Summary of Differentiation:
Good luck everyone!
Summary of Differentiation:
- Power Rule
- Product Rule
- F'(x) = f'(x) g(x) + f(x) g'(x)
- Quotient Rule
- Low D High, minus High D Low, All over Low Low (The SONG!)
- F'(x) = [ g(x) f'(x) - f(x) g'(x) ] / [ g(x) ]^2
- Chain Rule
- F'(x) = f'( g(x) ) g'(x)
Good luck everyone!
Monday, April 14, 2008
Late Scribe x2 and Bob
Well I dropped the ball here, haven't really been paying too much attention to this particular blog of late. So by Murphy's law I was picked as scribe. Alright this isn't my best work I can tell you now, but this is how those two classes I have to scribe for go:
Day 1:
The point of this class was to come up with the equations of tangent lines and normal lines.
-Tangent lines are lines touch that touch the graph only once on a certain interval (the graph may wiggle and the tangent line can cross the graph at another point that does not matter)
-Normal lines are lines that are perpendicular to a tangent line.
-Recall that the first derivative of any funtion gives the slope of the graph at any point
-To find the equation of a tangent line at a point on a graph you need a couple things
-You need a point and you need slope
-You may use slope-intercept formula if you are given the y intercept y=mx+b
-But you'll probably be using point-slope formula (y-y1) = m(x - x1)
-So the general method to finding the formula of a tangent line to a point goes something like this:
-Find the derivative of your function
-Evaluate at your point
-Plug it into point-slope formula
and presto! There's your answer!
To find the equation of a normal line (a line that is perpendicular to a tangent line) there is only one more step. When you find the slope you just need to take the negative reciprocal of that and then plug it into our formula.
The last question we had that class asks us to find when the tangent line is horizontal. Well that is when the derivative equals zero. So you come up with the formula of the derivative then solve for the zeroes. Then you plug those x-co's back into the original function to find the points where the tangent line equals zero.
Day 2:
This class is a little more complicated.
-Mr.K started off with a talk about questions that the answers to were that just because we don't know for sure doesn't mean that something is or isn't there or happening.
-The shadow of the balcony, we would infer that there is a balcony casting that shadow, doesn't have to be, could be something that looks like a balcony.
-Then is that roof insulated? Well there is melted snow in places so we could assume no.
-Then do those people agree with one another? Through the story of Mr.K since their body language is all somewhat the same they probably are, but we don't know for sure.
-We then found the derivative of a semicircle.
-Mr.K showed us that we could define this function in other ways to get an infinite amount of other circle bits-and-pieces functions (see the slides)
-This was to show us that there could be many functions buried within another and that even though we don't know which one there may be we have to treat it as if there is another function within it and therefor when we differentiate we have to use the chain rule.
-One thing to notice about this is that the derivative might be in terms of y and x so you may need a set of coordinates to solve for the slope at a certain point instead of just an x-co.
Bob
I feel fairly confident for the upcoming test. No worries at all really. Schedule should die down a little so I wont' miss any more scribes or bobs!
G'night! (might edit this sometime to add some examples but I am *really* tired right now so sleep is a must... after bio...)
Day 1:
The point of this class was to come up with the equations of tangent lines and normal lines.
-Tangent lines are lines touch that touch the graph only once on a certain interval (the graph may wiggle and the tangent line can cross the graph at another point that does not matter)
-Normal lines are lines that are perpendicular to a tangent line.
-Recall that the first derivative of any funtion gives the slope of the graph at any point
-To find the equation of a tangent line at a point on a graph you need a couple things
-You need a point and you need slope
-You may use slope-intercept formula if you are given the y intercept y=mx+b
-But you'll probably be using point-slope formula (y-y1) = m(x - x1)
-So the general method to finding the formula of a tangent line to a point goes something like this:
-Find the derivative of your function
-Evaluate at your point
-Plug it into point-slope formula
and presto! There's your answer!
To find the equation of a normal line (a line that is perpendicular to a tangent line) there is only one more step. When you find the slope you just need to take the negative reciprocal of that and then plug it into our formula.
The last question we had that class asks us to find when the tangent line is horizontal. Well that is when the derivative equals zero. So you come up with the formula of the derivative then solve for the zeroes. Then you plug those x-co's back into the original function to find the points where the tangent line equals zero.
Day 2:
This class is a little more complicated.
-Mr.K started off with a talk about questions that the answers to were that just because we don't know for sure doesn't mean that something is or isn't there or happening.
-The shadow of the balcony, we would infer that there is a balcony casting that shadow, doesn't have to be, could be something that looks like a balcony.
-Then is that roof insulated? Well there is melted snow in places so we could assume no.
-Then do those people agree with one another? Through the story of Mr.K since their body language is all somewhat the same they probably are, but we don't know for sure.
-We then found the derivative of a semicircle.
-Mr.K showed us that we could define this function in other ways to get an infinite amount of other circle bits-and-pieces functions (see the slides)
-This was to show us that there could be many functions buried within another and that even though we don't know which one there may be we have to treat it as if there is another function within it and therefor when we differentiate we have to use the chain rule.
-One thing to notice about this is that the derivative might be in terms of y and x so you may need a set of coordinates to solve for the slope at a certain point instead of just an x-co.
Bob
I feel fairly confident for the upcoming test. No worries at all really. Schedule should die down a little so I wont' miss any more scribes or bobs!
G'night! (might edit this sometime to add some examples but I am *really* tired right now so sleep is a must... after bio...)
Thursday, April 10, 2008
Tuesday, April 8, 2008
Monday, April 7, 2008
Scribe posts for: March 19 & 28
Hey everyone! I apologize for the super super late scribe post. I know you are all waiting for it so here it is.
March 19.
The class started off with a discussion about Article 13 and the students' comments on their class blog. Moving on from that, we reviewed the sum/difference rule and then moved on to the new topic. The class topic was mostly about the product rule. All the information about the class work and the rule and how to apply it is in the slides below. Also we learned about the quotient rule but we ran out of time so it was continued in the other class.
March 28.
This was our last class before the spring break. During this class we reviewed the quotient rule and Mr K. taught the class the quotient rule song. The song goes like this: "high de low minus low de high all over low low" which translate to: [f(x)^1 * g(x) - g(x)^1 * f(x)]/g(x)^2.
But this class' real topic was... an introduction to the chain rule! The chain rule basically states that the whole function is called F(x). This F(x) is composed but different functions which are f(x) and g(x) which g(x) is the inner function and f(x) is the outer function. If examples are need it is in the slides below.
Thank you for your time and I do apologize for the super super late blog post. Now that I finished this scribe post the next scribe shall be... GREY-M.
March 19.
The class started off with a discussion about Article 13 and the students' comments on their class blog. Moving on from that, we reviewed the sum/difference rule and then moved on to the new topic. The class topic was mostly about the product rule. All the information about the class work and the rule and how to apply it is in the slides below. Also we learned about the quotient rule but we ran out of time so it was continued in the other class.
March 28.
This was our last class before the spring break. During this class we reviewed the quotient rule and Mr K. taught the class the quotient rule song. The song goes like this: "high de low minus low de high all over low low" which translate to: [f(x)^1 * g(x) - g(x)^1 * f(x)]/g(x)^2.
But this class' real topic was... an introduction to the chain rule! The chain rule basically states that the whole function is called F(x). This F(x) is composed but different functions which are f(x) and g(x) which g(x) is the inner function and f(x) is the outer function. If examples are need it is in the slides below.
Thank you for your time and I do apologize for the super super late blog post. Now that I finished this scribe post the next scribe shall be... GREY-M.
Subscribe to:
Posts (Atom)
