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...)
