October 2nd, 2012
Scribe: Cooper

We started class today with a worksheet entitled exploration 3-3: Numerical Derivative by grapher. The main idea of the exercise was that we found points on the graph of the derivative of d(t) by looking at the graph of d(t) and using the symmetric difference quotient with a change in time= 0.001. To find the instantaneous velocity, or derivative of d(1) the equation would look like this: $$\left(f\right(1+d)-f(1-d\left)\right)/2d$$$$$$ To graph the entire function of the derivative of d, we used the nDeriv button (found in the math section of the calculator) and then plugged in x as a variable. So, before hitting enter and finding the function of the derivative of d(t) the screen on the calculator should have looked like: nDeriv(y1,x,x).
We continued to talk about the use of calculators a little bit and got into using the solver function. To get to solver, hit the math button, and then find solver. Next we can enter any Y value for which we want a certain function (which is entered as y1, y2 etc) to equal. In order to solve for x, you have to enter in a guess. Be careful with this guess because it actually has to be near the correct value for the application to solve the equation correctly. Next, hit alpha enter to actually solve for the variable.

Point of inflection: Next, we found the point of inflection on the graph of the derivative. The point of inflection is defined as the point where the slope of the graph of the derivative switches from getting bigger or smaller, to the opposite. Physically, the point of inflection is apparent where the line switches from being concave upwards to concave downwards, or the other way around.

Next in class, we got our tests back. Do super duper corrections, and study for the 40 minute test on thursday!!

After taking a gander at our super corrected tests, we steamed ahead by looking at the Damian (power) rule, as well as solving for the function of the derivative using the definition of the derivative. So, the Damian rule states that to convert the function d(x) to d'(x), you first multiply all coefficients with their corresponding powers: this is the new coefficient. Then drop the power by one: this is the new power. f(x) = xⁿ is f ’(x) = nx^n-1.
We then proved that the Damian rule worked by plugging the function f(x)=x^2 into the definition of a derivative.

http://www.sosmath.com/calculus/diff/der01/der01.html

UPDATE: Alternate form of I'Hopital's rule:

We ended class by learning two new rules, each pertaining to the addition and subtraction of derivatives. The rules state:

 

http://www.math.brown.edu/UTRA/derivrules.html