Well back again for another scribe, sorry that this scribe is late I had other homework. Well we began class with the derivative problem from Friday which we were not able to finish. A good thing to remember when doing a square root derivative problem is that it is always nice to break it into pieces. So for the first question which is asking for the derivative between x and x^2 it is easier to find the value of 0-x and then the value of x-x^2. Due to the fact that it is easier to find a derivative of 0-x. So 0-x first must be reverted to x-0 so that we are able to find the derivative which means that that part of the equation is going to be negative. As you can see on the slides Mr. K had posted, it is much easier to differentiate with 0-x then x-x^2. So you solve by placing x in for t and then find the derivative of x^2 which is simply 2x.

For the next question we are trying to find the area underneath the graph to the x-axis. It is not as hard as it seems. To begin take the equation that is given and find its roots. (To find the roots it is much easier to use synthetic division which is shown on the slide). Once the roots are found the next step can then be followed. As the next step is shown in two different ways, here is the first way explained. When finding area it is not signed area instead is is all the are including both positive and negative. Which means that when evaluating the equations to solve for area you must break up the positive and negative areas in two equations. Then take the positive equation and subtract it by the negative equation so that the negative equation changes sign to positive and the areas may be added. The second method is by evaluating the who equation over the whole interval and then taking the absolute value to receive both the positive and negative area.

For two graphs you follow the exact same procedure, except you are also subtracting the lower graph from the upper graph when finding the area in an set interval, before subtracting the total negative area from the total positive area.

That was basically the whole class. Tonight's homework was 6.4 (all the odd #) and remember to bob before Thursdays test, so that also means pre-test Wednesday.

Tomorrow's Scribe is TIM!

## Monday, December 17, 2007

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